Try unsoldering the reset button and see if that helps. That's the I can think of right now...
Although it might be as you say, that the reset circuit has locked up. It might be a broken capacitor or transistor.
4MB Mega/STE with FreeMiNT/XaAESm 40MB SCSI HD, 1.44M floppy
Recased Falcon030 with CT2, 64MB TT-RAM, 4MB ST-RAM, FreeMiNT/XaAES, EtherNEC and 40GB HDD