You got it right Feef! Well, except for the ROM Stick; the IIcx ROMs are on sockets on the motherboard, not on a stick like a IIfx though there is a ROM SIMM Socket to put one in with a jumper to set it.
This looks like RAM Problem from way back then. You can run the IIcx on 1 bank of RAM on Bank A, so use that to test what you have. The IIcx can run as little as 1MB RAM (4 * 256MB SIMMs). The RAM should be 100ns RAM or faster. It can take 120ns RAM but it will run slower, and 150ns RAM wont work on it as I remember.
Inspect the RAM Sockets, make sure that the clips are not cracked or broken, that there are no corrosion on the pins, and that they are solder to the mother board cleanly and securely (you need to remove the mother board from the case to check the underside of the board).
I have a board with broken clips, but with a cardboard spacer I can secure the SIMM to be upright with the one before it to test it out. It works once the SIMM is upright, but its not a fix to a problem, just a test of the socket itself. Eventually that board needs to get its RAM SIMM Sockets replaced.
With a mulitmeter you should check the traces from SIMM Socket to SIMM Socket - out of the 30 something pins, 10 will not connect to the other sockets for they are data, and other function lines.) So you should have at least 20 pins that should check out to their respective banks.
Inspect solder joints with a magnifying glass, clean up any corroded joints by desoldering and resoldering it. Thing is, the Tin may have leached out from the corrosion, making it a higher lead content that is harder to melt. You would need to add solder to get it melted and then remove that solder when you got some of it melted and add more solder and remove that - repeat until the joint is completely desoldered and clean it up with some acetone before resoldering.
Once you get it to Chime without a Chimes of Death, you can set up your RAM to its max you can get it too, and add the floppy and hard drive.
You should also recap the video board, there are about 6 caps at the bottom of the video card that needs replacing and one or two in the middle of the board.
This looks like RAM Problem from way back then. You can run the IIcx on 1 bank of RAM on Bank A, so use that to test what you have. The IIcx can run as little as 1MB RAM (4 * 256MB SIMMs). The RAM should be 100ns RAM or faster. It can take 120ns RAM but it will run slower, and 150ns RAM wont work on it as I remember.
Inspect the RAM Sockets, make sure that the clips are not cracked or broken, that there are no corrosion on the pins, and that they are solder to the mother board cleanly and securely (you need to remove the mother board from the case to check the underside of the board).
I have a board with broken clips, but with a cardboard spacer I can secure the SIMM to be upright with the one before it to test it out. It works once the SIMM is upright, but its not a fix to a problem, just a test of the socket itself. Eventually that board needs to get its RAM SIMM Sockets replaced.
With a mulitmeter you should check the traces from SIMM Socket to SIMM Socket - out of the 30 something pins, 10 will not connect to the other sockets for they are data, and other function lines.) So you should have at least 20 pins that should check out to their respective banks.
Inspect solder joints with a magnifying glass, clean up any corroded joints by desoldering and resoldering it. Thing is, the Tin may have leached out from the corrosion, making it a higher lead content that is harder to melt. You would need to add solder to get it melted and then remove that solder when you got some of it melted and add more solder and remove that - repeat until the joint is completely desoldered and clean it up with some acetone before resoldering.
Once you get it to Chime without a Chimes of Death, you can set up your RAM to its max you can get it too, and add the floppy and hard drive.
You should also recap the video board, there are about 6 caps at the bottom of the video card that needs replacing and one or two in the middle of the board.