Could be the overvoltage protection relay. Its a quick and easy job even for someone with no experince. It should be located along the firewall, a little silver box with a clear plastic cover and a red 10amp fuse in it. Check the fuse first. If it is good you may need the OVP relay. Mine cost $65 with tax (Canadian dollars) they just pull out and plug in. Many people on this forum have had problems similar to yours and fixed it with a new OVP. On the other hand a number of things could cause this problem, and there is no guarantee that the OVP is your problem.
1995 E420 - retired
1986 420SEL - retired