The IIciIIcx are 32bit machines so 2-SIMM configuration will never work on these machines as that is a 16bit configuration.
16MB SIMMs? Trying to achieve 64MB/128MB IIci? I would suspect them. If Uniserver recapped the machine, that means that he had tested it on his RAM and his PSU, I know he guarantees his work.
Try 4MB SIMMs to get 16MB on Bank A and see if it works. If the problem persists, then it's the PSU needs recapping. You checked the voltages coming out of the rear floppy port?