Try booting while pushing down with a plastic thing (little pressure) on the 68060.
Also try tipping the caps-lock key:does it keep going on/off?(after about 7 strokes)
If not the procesor/socket is likely to blame.
I dont think it is the processor itself what gives the problem but the socket.
I managed here to build me a support bracket which pushes it down towards the print in a tower.
Works for now but already send a e-mail to amigacenter in france to get me a new socket.
I think it is the only place where these can be fixed with expertise.
In my case a 68060 on a cyberstormppc
goodluck!
