Ah, yes, that sounds like my 'dead' A600.
I'd given it up for dead, poor little thing. It would power up the screen (which would stay black), the disk drive would give one very small gronk as power was applied to it, the Caps Lock light would come on, and it would sit there.
And sit there....
And sit there....
I took out all the expansions, HD, FDD, RAM etc.
It sat there.
Nothing on the mobo to be fixed, I gave up and put it all back together.
A few weeks later, I felt like trying it again, as sometimes these things sort themselves out, so I fired it up. No change. It sat there. So I left it there to sort itself out. It just sat there.
About 5 hours later I rememebered I'd left my A600 doing absolutely nothing on its own so I went to turn it off... but wait! There was gronking! The Caps Lock light had gone off! Quickly connecting to the TV, there it was - Kickstart 2.05 ready to boot! Joy! Quick, get the HDD and RAM expansion back! Everything back in.. and it worked! It booted straight into WorkBench, 2MB RAM and all.
The next time I went to use it, it just sat there. And sat there.. until an hour later, it fired up! From then on it was fine and normal... at least until the next time I went to use it....
To this day it takes an absolute age to fire up the first time each session, though I think the time is getting smaller as I swear it was up and running just 15 minutes after applying power last time!
So that's my experience. Maybe you'll find something useful in there, maybe not, but the moral of the story is that patience can be rewarded with A600s, I guess....
