First of all that old supply wouldn't even meet the minimum requirements of any recent board out. What was a 180-250w supply at best? You would need at least an atx 300w not an old AT type underpowered supply just to see a post.
It's likely that other things besides the supply failed on that old of a system. If the board had a battery to maintain the cmos that's probably long gone charly there. The board itself could have easily given out as well.