You're a newb, but that's ok - we all started out that way, and the only way to learn is with some edjamakashun!
So, today's lessons:
When a slot-load optical drive spits out a disc without providing any notifications on the computer's screen, it generally means that the drive can't make any sense of the disc whatsoever, and since it can't do anything with it, the drive spits it back out. Tray-loading drives that can't figure out a disc will just sit there; they won't do anything until you manually open the drive. The slot-load ejects the disc instead of just sitting there, mostly because there's really no eject button to otherwise extract the unread disc.
If you're having issues with recorded CD-Rs, but normal CDs work fine, it may just be the fact that the drive doesn't like burned media. Some drives don't. If, on the other hand, some burned CD-Rs work and some don't then it may be a problem with your burning software or the brand of disc.
If it doesn't like to read CDs regardless of whether they're manufactured or burned (CD-R or RW), then it's probably an issue with your drive. You may want to try using one of those CD cleaner discs through it and see if that helps.
The two similar jacks on the side of the iMac may look the same, but they're very different. The smaller one is called RJ-11, and is used by the internal modem. There should be an icon of an old telephone handset with some kind of dot/line pattern coming out of it. Use this port if you're dialing up. Otherwise, ignore it.
The second port is called RJ-45, and this is your Ethernet port. It should have an icon that looks like this: <***> This port is for high-speed network connectivity, allowing you to join 10 or 100bT Ethernet networks, and to connect directly to devices such as cable or DSL (broadband) modems. Use this port if you've got a broadband ISP.
Word of caution: don't plug the phone line into the Ethernet port, or you may damage the Ethernet circuitry in the computer (and, with the iMac, you'd have to replace the logic board to fix it). Phone lines generally transmit higher voltages than Ethernet, especially with incoming calls.
As for the broadband modem, it may have two different connectors on it (three, if you count the incoming phone or cable jack): an Ethernet port, or a USB port. If it only has an Ethernet port, skip to the next paragraph.
If it has a USB port in addition to an Ethernet port, ignore the USB port - you'll most likely need special software to run your internet connection through USB, and Ethernet is faster besides (at least on your iMac it is).
To use Ethernet to connect your iMac directly to your broadband modem, you'll need a proper Ethernet cable. If you're using the one from your PC, you should be fine - from what I gathered from your post, your PC currently connects directly to the modem, so we're just going to mirror that setup.
After plugging in the modem to your iMac's Ethernet port (and ensuring that your modem is operational), since you're in OS 9, you'll go to the TCP/IP control panel. In there, you'll go to the "Connect Via" drop-down box and make sure that Ethernet is selected. Then in the "Configure" box, you'll chose "Using DHCP Server" (if you don't know what DHCP is, we can cover that later). Then, just close out of the control panel.
Try opening Internet Explorer (or whatever browser you've installed, OS 9 usually included IE and Netscape).
If it works, good. If not, let us know and we'll go from there. If it doesn't work, you might want to wait a few minutes or an hour and then try again, maybe restart the computer. It may work when you come back. Ya never know with some stuff.
So, today's lessons:
When a slot-load optical drive spits out a disc without providing any notifications on the computer's screen, it generally means that the drive can't make any sense of the disc whatsoever, and since it can't do anything with it, the drive spits it back out. Tray-loading drives that can't figure out a disc will just sit there; they won't do anything until you manually open the drive. The slot-load ejects the disc instead of just sitting there, mostly because there's really no eject button to otherwise extract the unread disc.
If you're having issues with recorded CD-Rs, but normal CDs work fine, it may just be the fact that the drive doesn't like burned media. Some drives don't. If, on the other hand, some burned CD-Rs work and some don't then it may be a problem with your burning software or the brand of disc.
If it doesn't like to read CDs regardless of whether they're manufactured or burned (CD-R or RW), then it's probably an issue with your drive. You may want to try using one of those CD cleaner discs through it and see if that helps.
The two similar jacks on the side of the iMac may look the same, but they're very different. The smaller one is called RJ-11, and is used by the internal modem. There should be an icon of an old telephone handset with some kind of dot/line pattern coming out of it. Use this port if you're dialing up. Otherwise, ignore it.
The second port is called RJ-45, and this is your Ethernet port. It should have an icon that looks like this: <***> This port is for high-speed network connectivity, allowing you to join 10 or 100bT Ethernet networks, and to connect directly to devices such as cable or DSL (broadband) modems. Use this port if you've got a broadband ISP.
Word of caution: don't plug the phone line into the Ethernet port, or you may damage the Ethernet circuitry in the computer (and, with the iMac, you'd have to replace the logic board to fix it). Phone lines generally transmit higher voltages than Ethernet, especially with incoming calls.
As for the broadband modem, it may have two different connectors on it (three, if you count the incoming phone or cable jack): an Ethernet port, or a USB port. If it only has an Ethernet port, skip to the next paragraph.
If it has a USB port in addition to an Ethernet port, ignore the USB port - you'll most likely need special software to run your internet connection through USB, and Ethernet is faster besides (at least on your iMac it is).
To use Ethernet to connect your iMac directly to your broadband modem, you'll need a proper Ethernet cable. If you're using the one from your PC, you should be fine - from what I gathered from your post, your PC currently connects directly to the modem, so we're just going to mirror that setup.
After plugging in the modem to your iMac's Ethernet port (and ensuring that your modem is operational), since you're in OS 9, you'll go to the TCP/IP control panel. In there, you'll go to the "Connect Via" drop-down box and make sure that Ethernet is selected. Then in the "Configure" box, you'll chose "Using DHCP Server" (if you don't know what DHCP is, we can cover that later). Then, just close out of the control panel.
Try opening Internet Explorer (or whatever browser you've installed, OS 9 usually included IE and Netscape).
If it works, good. If not, let us know and we'll go from there. If it doesn't work, you might want to wait a few minutes or an hour and then try again, maybe restart the computer. It may work when you come back. Ya never know with some stuff.