The IIsi, due to it's design where the speaker is directly below something THAT VIBRATES A LOT (*cough* hard drive), will commonly have a faulty speaker. Check the solder points at the speaker's voice coil wires, and check the condition of the contacts at the motherboard end (in the IIsi said contacts simply touch the MB).

I have a Griffin Sync Adapter, which is supposed to separate the IIsi's Sync-on-Green video hardware, but all of my non-SoG monitors refuse to sync and display. Only my SoG display (an LG FlaTron W2043T) reliably syncs to the IIsi. I'd get a monitor that natively supports SoG-it seems that many Flatron's do, so I'd start there. You can probably get one on eBay for $25. Or just get an Apple HiRes RGB display.