the A4000T (amiga version - not modded A4000D) had the chip ram souldered onto the mainboard, and the battery isn't really an isse so that should be cool.
a Cyberstorm1/2/3/PPC equipped machine _WILL_ boot with no fast memory installed, do this to check its not dodgy memory... do any of the simms get real hot real quick after turning on? (obvious sign of dead ram chip). tho it might be good to stick a known good simm in a mainboard slot just to help it out (it will be dog slow tho

remove all IDE/SCSI devices and set termination accordingly.
power on, and after a few seconds to half a minute, does the floppy drive click? (the machine polls the drive to see if its got a disk in there). this indicates that the machine has passed all power on/reset tests has probed the scsi and IDE busses looking for devices with bootable partitions, couldn't find anything, and is waiting for a bootable disk/drive even if there is no video (duff I/O board)
as you said the the caps lock light was working, i take it then it wasn't flashing by itself? there is a document somewhere that explains not only the amiga's boot colours, but the caps lock flash sequence too for trouble shooting
i can't think what else to check other than the CPU/BUS clock jumpers (for Cyberstorms, both set to external. numbers J101/J104 i seem to remember. prolly wrong there :-) )
the mainboard is properly mounted and not shorting against the case? the CPU board is mounted with those plastic standoffs, and not just hanging off the CPU slot? ;-)
if you sniff the mainboard, nothing smells burnt?
it could be your PSU is cooked. tried another one? My A4000T CybPPC with a shed load of zorro cards had eaten about three PSU's in the time i had it. (the drives were run from another PSU.. there is space enuff in the case for two.)
anything else i can't think of at the moment... good luck!
----additional thought----
whenever i booted with DF0: disconnected, it would boot, but complained about no disk in device DF0: and workbench would show "DF0:

?" so as for not booting without a floppy drive, you got me there....