Check and remove the earth strap from the starter [or elsewhere on the engine] to the body of the car, [right hand side rear when looking at the back of the car] this is a very troublesome connection, it may look ok, but it can cause serious resistance when it hasnt been cleaned in a while, once cleaned up, use copper slip on the connections when re-assembling, this will help maintane the continuity.
If you have already checked this then ignore my comments.
Good luck.
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