If it is a short, there should be fuses blowing. Having a bad ground will definately cause this type of behavior. I had problems just like this and more with my 93 a short while back, and there were several grounds that had been taken loose to replace te engine, but had never been put back.
I looked and looked and looked for months before I finally took it to the dealer and paid them 150 bux to track down and fix the problem. Several ground wires later, all is fine!