relay problem between battery and electronics

[0h n0 5.0]

hey guys, got a 94gt, auto, realtively stock, new exhaust, no aftermarket ignition.. whenever i go to do somthing electrical: turn on lamps, windows, radio, start the ignition.. it kills and won't turn over. i think it might be a relay beween the battery and the electronics controled by the eecIV. the battery is relatively new (i.e. theres is no signs of corrosion on the posts) but i do not really know how old it is since i got the car used and this has jus begun to happen recently, i've only gotten it started like this once before by removing the posts, and re-clampin the suckers tighter. its really annoying and i'm afraid to drive it somewhere for fear of bein stuck cause a f'd up fuse. any insights ya got would be marvelous.

[Hozer 88GTConv]

5.0? If so, does it only do it when the engine is warm?
The only reason I am saying this is OEM 5.0 starters are known to conduct heat and as a result, when the car is warm, tend to draw too many amps and will not turni over until they have cooled down sufficiently.
I only know this because mine does it and I need to replace it with a high-torque aftermarket starter.