Given that you get a chime with the SE/30 and IIfx ROMs, I think you might try one of Doug's custom ROM modules. Check the Hacks forum. You'll want it programmed with IIci code, and if you just need a usable IIci ROM, then you don't need the fancy 8 MB version. The version 1 boards, if he still has some, will do the trick.

I had a similar problem with IIci ROMs. The extracts I made to repair the problem are here:

http://www.prismnet.com/~trag/Firmware/IIci/

Maybe Doug can put the code on the chips for you.

Still, it's a good idea to replace the caps under the power supply in any event. Those are what killed my first IIci back in the mid-90s. Ate through a via and it was a bear tracking down the problem.