I'm pritty sure the A500 only have a 50W PSU. Anyway, I got an almost identic setup (A1200, B1260+extra coolingfan, Scandoubler, Melody1200Pro, external diskdrive, A500PSU). The problem is that the PSU isn't powerfull enough to drive all of the Amiga and you realy need to change the PSU before you burn the one you got (I've already aquiered a 230W and is thinking of plunder the original A1200 PSU for it's power connector).
I got the same problem as you got with it sometimes going on without any hickups (usually when it's been off for like over night) else it needs to power upp the conds and stuff first (takes a sec) then turning the computer off and waiting for about 0.5 sec the HD led will light up a little and then is when you turn on the puter again.

It's a recepie for killing the computer and/or extra addons so find a better PSU as soon as possible.
Ps. If I try to connect anything else like a CD, the SurfSquirrel, a PCMCIA Ethernet card it won't start at all so I'm at the edge of what my PSU can handle before giving upp... 2H into use it's almost so hot one can't touch it. :-D