Your Miggy have an internal hd? If yes, the black screen is normal when you have a unvalidated partition. Just keep the Amiga on for up to 8 hours to allow the kickstart program to fix the problem for you.
The Amiga have a proprietary mouse, you can't use any other type of mouse without a converter.
Other chance is you have a bad PSU, or the capacitors on the motherboard and in the PSU have dried. It's an inexpensive fix, will only cost you a few bucks and some patience.
Plus: do you use your 1200 with a tv or a monitor? Amiga monitors are 15kHz. Modern ones can't sync to a lower frequency like that...
