I agree with Machine Man's analysis. The key for me was the statement "it would start as you let off the ignition switch". With the starter motor engaged, voltage on a stress system is reduced, and when you let off, the voltage rises enough to get it to catch. I've seen similer on several other cars over the years. The recommendations to check the grounds are excellent, both at the battery and at the connection to the body and engine as well as other various key components. I had a friend replace the starter twice. I kept telling him to check the ground, he did, but at the battery only. The corrosion was underneath the fitting where it mounted to the body. Good Luck!

Jerry
01 V70 T5