Don't look at anything except the fuel pump relay. Then. after you have looked at it, take it out, open it, resolder the bad joints, stick it back in and turn the key. Then if it still doesn't go, it is most likely the transistor controlled ignition module. They are cheap on ebay but cost thousands in dealerships.
Please let us know what happens.

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Andrew
300e 294,000mi
380sel 185,998mi
380se 309,980mi