Points on pressure switch stay in the closed position and won't kick out when pump stops, therefore the pump won't restart. Have any ideas?

What do you mean? If the points don't open the pump doesn't stop.

Older house it's been vacant all winter water has been turned off at main, ex owner has been tampering with pressure switch, when I moved in last Friday no water. Sometimes pump seems to work, pumps up to 40 pounds. Later on no water and gauge at 0. points on switch are in the pump position if you will and nothing happening. I have held points away for a minute then released and it would pump (sometimes) a lot of rust in lines, most are plugged, I took switch off this morning cleaned the best I could and nothing, hope it's not the pump?

Start by replacing switch. Lest expensive. Let us know how this works out for u. If still problem we can go from there.

Chuck

Are the contacts pitted and sticking together? If so you can clean the contacts with a file or sandcloth or you simply replace the switch. Good luck, Tom