A solenoid is a relay, if it's bad or marginal it won't pull in the main circuit. Sometimes you can hear if the solenoid clicks, if it clicks but doesn't turn it's the starter motor.

If the timing is too far advanced it will make it worse. You can take the starter in for a load test at many auto parts stores. Or swap the old one in.

Also check all the cables...battery to engine ground, battery to starter positive especially, and that the starter bolts are tight.

I just use the stamped factory heat shield, but there are modern insulating jackets that probably work better.