[rpmerf]

Firstly, verify the battery is actually the problem. I would consider the battery dead if it drops to less than 10v while cranking. Batteries don't recharge themselves from nowhere. This sounds like a starter issue to me.

I would -
Make sure the connections at the battery are clean and tight.
Make sure your grounds are installed to a clean place on the block and tight.
On my truck, I ran a ground directly to the stud on the back of the starter.
Make sure the positive wire is clean and tight on the starter.
Check that your starter signal wire is getting 12V.
If all else fails, replace the starter. Many have said the gear driven starter from a 98 Tahoe is a good upgrade. Takes less power and turns the engine over faster.