something is wrong with my car

[hulkster_s13]

i have a 90 s13 w/blktop sr20. problem is that my battery dies overnight. but also i have a fuse remover with a check light on it that shows if the fuse is good,when i check the fuses, the light on the removal tool lights up and then dies out.my other car the light stays on. this happens on all fuses with car on or off. im wondering if this is signs of a short?bad alt, or bad battery. it first happened to my optima red top, then i got a die hard bat from sears and it did the same thing again. also when i push my brakes my radio illuminates while car is off. the radio is not ghetto rigged in there. my radio is hooked up to the stock wiring with a harness adaptor. any help would be much appreacited<sp? i slao rewired my whole car thinking that that was the problem. after rewiring my car still does it. please help