I just picked up a 87 535i a couple days ago. The car has been sitting for a while and I am in the process of getting it cleaned up and assessing its condition. The first problem that I have encountered is a weak connection with the battery. When I connect the fully charged battery I do get power inside the car but it instantly dies once I try to start the car. When I have the battery charger connected the lights inside the car get brighter and more of the accessories will work but still a extremely weak connection. I have cleaned both of the battery terminals with no change. I just need to know what main places I can check for bad connections that could cause this. The dash lights, headlights, interior lights will all work fine. There is not enough power for any of the power stuff and for sure not enough to start the car.

ground cable connections (small ones too) at chassis
ground strap at motor mount
DME ground cluster by #6 fuel injector on head
small ground to valve cover to firewall.

Thanks for the quick reply, I lack the needed daylight today to do anymore with it so I hope I can get something happening tomorrow. I have high hopes that I can bring this car back to life.