Not sure about the IIci, but some old Macs need a working Lithium battery in order to startup.
Maybe you could try to put near 5 V between pin 9 of the PSU connector and ground -- a similar procedure can be used for starting up a Mac IIx.
Maybe you could try to put near 5 V between pin 9 of the PSU connector and ground -- a similar procedure can be used for starting up a Mac IIx.