The PSU you use probably droops like anything if it's only rated at 300ma, hence the blank display.

Monentary voltage drops will cause a reboot - well, starting your engine is generally at least 1 second of cranking, which gives a huge voltage drop (below the 8v level where the PSUs will still work). This is totally expected - every car radio I've owned has reset during cranking the engine, it's just that the empeg takes a little longer to reboot.

Hugo