That's... very weird.
The fusebits set and then an error is characteristic of the fusebits being set wrong in a way that broke the board. But you're using an 8mhz pro mini which should have external crystal (besides, that gives signature of 0x000000, not target didn't answer), so what other setting could be breaking the board?
Say, measure the voltage on it's vcc with it connected to the USBAsp... Are you really getting 3.3v on vcc? (if it's undervoltage enough to trip the BOD, maybe that would give that error?)