I encountered similar way back (9 years ago - I bought a 1230 MKIV + 40 MB 60ns RAM to celebrate having cash left at the end of my first year of uni - shows ho long ago this was - finishing a year of uni without debt! Ah those were the days...never mind, get back on track)
I had an Archos Overdrive 35 plugged into PCMCIA which wouldn't be seen if I didn't disable the accelerator, which is really strang as I believe that the problems of RAM expansions using the same address space as the PCMCIA DID NOT occur if the expansion was part of a CPU-based accelerator (as opposed to just FAST RAM acceleration).
At the time, I got around it by buying an IDE interface and transplanting the IDE hard drive from the Overdrive into the case - not ideal for your solution, but read on...
I upgraded to a 32MB 60ns simm about 5 years ago and since then I haven't had a PCMCIA problem - I'm running a network card from it now (don't know if the Overdrive works). I hope that this helps. In the short term, have you tried the Kickstart into RAM jumper in the position that it isn't in now? Can't guarentee, but it MAY work - worth a try.
Oh yes - I don't think it is a power problem as the Overdrive 35 had its' own 12v PSU.