Yes, floppy drive connector needs to be connected - else the machine will either not show the Kickstart screen OR take an inordinate amount of time before it finally does.
Sounds like your power supply may be getting weak.
Did you try re-seating all your chips? Especially the CPU, Kickstart and CIA's...
BTW: I'd install your SCSI card in the closest slot to the CPU. Memory board to the left of it. Good general practice anyway, but may also indicate that you've got a power supply problem. How is the system without the RAM card installed?
Somebody here is selling an A2000 power supply for $25 + shipping. Every big box Amiga owners should have a backup if they don't know how to restore theirs:
http://www.amiga.org/forums/showthread.php?t=55197&highlight=amiga+2000+power+supply
