is that a reman or a new one?
Also, for future reference and for anyone searching the site, the easiest and simplest way to test a starter is with a test light.
Test light clip end on a good ground(power will light up the tester), touch the main big terminal on the starter. If it lights, you know, 3 things. Test light is good, ground for the test light is good and you have good power to the starter at the main wire.
Then move the probe end of the test light(pointy end) to the smaller terminal. This should not be powered at all now.
Now, have someone try to crank the engine with the key. it should now be lit as it would be at the battery itself. Nice and bright. Even if the engine does not turn over, this terminal should still be getting power.
Now, you have taken all the guesswork out of testing ANY other part of the system. Right from the key, the ign cylinder, the ign switch, all the wiring, relays, connections etc all the way down to the starter itself.
So, if you have power at the main one, and power at the small one when the key is in "start" you need a starter.
Oh and another point for reference. the starter does not have its own ground. They are grounded by the large bolts holding it to the engine/transmission, depending on the car.
I have a great story about test lights for starters.
My Mark 2 Jetta has been a tank, so It has been my backup car or daily driver for the last year and a half while I've had various tempermental or problematic cars.. I can always count on it.
One day it just didn't crank. The symptoms were actually similar to Chad's starter issue but very infrequent. I would take 4-5 trips a day 7 days a week and it would only happen about twice a month. So I would get out and bang on the starter a bit, which worked once or twice but this never really seemed to do anything. Usually I would just push start it (I always parked facing down a ramp) or would take my other car, and the problem wouldn't come back for weeks or even months. I figured it was just a dead spot in the starter at this point.
About 5 months had gone by and one day I was bored enough to bother troubleshooting it. Applied 12v directly and it fired the starter perfectly over and over again, and I couldn't replicate the problem. Spent about 3 hours sitting around having a drink and restarting that poor car about 100 times over the course of a night
I gave up for a few weeks, and then one day I couldn't get it started and wasn't in my usual spot so instead of push starting I ended up running a jumper wire from the battery to the starter and starting it manually.
Now anyone that knows older VW's know that they really only have one "common" trouble spot which is the ignition switches like to go bad. The previous owner had replaced 2 in my car, one just before I bought it so naturally I figured it was likely to be the switch given that the starter never failed with voltage applied manually.
So I did what John mentions - I rigged up a test light. To connect it to the starter I had to take one end of the thick gauge wire and shove it in to the spade connector clip on the top of the starter. After that, it worked all night so I eventually just ran the test light into the cabin so I could wait for it to fail and would immediately know: Ignition switch, or starter.
Fast forward 8 months later, It has never had the problem again
Turned out it was just a lose fitment in the signal connector, and the "test light" is still there because it's now know as the test light that kept my car running.