I had this blank screen issue happen to me a couple days ago, with my LC II. I thought maybe it was the fault of the cable I was trying to use with my scsi zip drive (a DB25 M/M cable, somewhat thicker than a normal parallel cable but unlabeled), because it happened after that. I tried booting the computer with the hd, floppy or both disconnected and I got the same problem though, which made me wonder about a different cause. I got some unusual extra sounds after the startup chime, too. However, after unplugging it and turning it off, I plugged both drives back in and left it unplugged. The next day it started up just fine...
Is this blank screen thing reliably connected to capacitors on the board and power supply? There might be a little gunk on the logic board, but I couldn't be 100% sure it was leakage -- the board in my LC II is a little dusty to begin with.
If it's helpful, I can take a couple pictures of the board, although there's nothing out of place that I can see.
P.S.
I bought a nice LCIII board to swap out with this one the other day, but if this is a power supply issue, I'd rather get that fixed...