2000 Chevy Lumina wont start

No previous problems. Parked car, tried to start later, no go. Key on, all inst panel lights and worning bells work, radio and lights also. Turn key to start position and nothing, no attempt to turn over, no dimming of panel lights. Checked battery with resistance type tester, good voltage. Cleaned battery terminals, still no go. Hooked up a remote starting switch to starter and with key in on position the engine cranked and started, but only ran for 3-4 seconds. Immediately tried again, and engine would crank but not start. Waited 2-3 minutes and engine started and ran 3-4 seconds.