92 Cutlass Supreme Intermittent Starting

I have 92 cutlass supreme Sl 2dr. 3.1 with 180,000K. When I try to start it I can hear the starter solenoid "snap" into place but it may or may not turn over. All interior lights/dash are lit up. I have replaced the battery and a recondioned starter. The wires and grounds all look good. When it does turn over it turns over freely with lots of juice. I have an old auto start in the system but bypassed and I have checked the byass switch and it is ok as it still may happen with the switch bypassed. Is there any other elec. parts that may be the problem(Ignition coil or module). Where are these parts situated on the car?Is the starter a bad replacement from Canadian Tire? Any help would be appreciated.

If the starter attempts to crank and fails, it is either the starter, the engine is binding up or a bad ground or battery connection, based on your description.

It was doing the exact same thing before I changed the starter. Is there two seperate current flows to the starter, one to engage bendix and one to give turning current to starter?:confused:

The ign switch powers the solenoid egagemment, but the large battery wire powers the starter itself.

"Wires and ground look ok" Don't go by look. Lots of wires get corroded under the sheath. Just because the dash lights light up doesn't mean anything. Very little current to light up the lights.