What do you have it connected to? If you are certain it is connected properly, then try the following (in this order if you wish):
-Remove any RAM cards from belly
-Reseat the ROM chip
-Remove the HD (A faulty drive will lock up, happened to me)
-Remove the shielding to see any obvious damage
Anything short of that you may have a dead A600. Contact Amiga Center of France if you wish to repair, or buy another from Europe (It's cheaper!)