1988 740 Turbo

I've posted on here before, but I've very little progress since, so I was hoping to get some new perspective on this..

Here's a brief history of what's going on:

-Used engine swap due to engine blow out
-Car ran strong before, including turbo
-When I got the car back, I was having hot start problems
-Once the car would get so hot, it would die
-Diagnosed and replaced fuel pump relay; radio suppression relay was ok

So here's where I start to get stumped. I swapped out the fuel pump relay, but the car was dead, so I got a jump and it fired right up. Since I've started to have the hot start problems, once I revved the car up to about 3500 RPM, it would "stutter." I kept doing that in neutral and eventually the car died again, needing a jump. The relay also started buzzing once it died. I was told the most common cause for a buzzing relay was a corroded positive bettery cable, but that doesn't account for the stuttering at 3500 RPM. Is my turbo going bad? I've never dealt with a turbo vehicle before, so could a malfuctioning turbo be draining the battery, thus causing it to die?

I'm starting a new job soon where I have to commute, so any help is much appreciated.