98 Cavalier 2.2 Cooling system nightmare

Problem started with low coolant light. Checked and coolant was leaking from weep holes in water pump, replaced it, flushed system, refilled, got all the air out and ran great for 2 days, then it overheated and theres no heat inside. I refilled the system got all the air out, ran it & it overheated and still no heat inside. Replaced thermostat, filled system, bled all air out, and still no heat/overheated. I was getting frustrated, so I flushed out the heater core, it is completely open, good flow. I then did the engine itself and again, good flow, flushed out good. I then did the radiator, and again good flow, no problem. Put everything together, filled system, bled out the air, and overheated/no hot air. Had it pressure tested. and held good pressure. Had the Mech. check the head, and compression test was good. There's no oil in coolant, no coolant in oil, motor doesn't run rough, no white smoke, I've eliminated the head/head gasket. Now I have thermostat out, ran a new hose and eliminated the heater core, filled system, got the air out, and it flippin overheated!!! I put a " T " in the new hose with a cap, so I opened it while motor was running(If water pump was working water should come flying out right?) and there was no water movement.....After all I've gone through, could my new water pump be garbage? any help would be appreciated...

Quite possibly, I have gotten more than a few bad parts, brand new frozen up calipers, bad thermostats, wrong size brake pads, lots of fun stuff to find out AFTER you put it in...

It's like 15 degree's out here, snowing like crazy, I have no garage, and need to get this car running....Is there any way to know if the water pump is working without actually taking it out?

Well, problem solved....Car runs great now....

Well, problem solved....Car runs great now....
what did you find was the problem?

Oops...Sorry, forgot to put it here. When I tore it apart, and pulled the water pump off, the impeller(Thing that spins and pushes the water through the engine) was seperated from the shaft. It is pressed onto the shaft, without anything to make sure it stays there, and in my case (rare as it may be) My brand new water pump was defective (www.asc-ind.com (http://www.asc-ind.com)) which was made by these fine folks I recently emailed to thank for their wonderful product (I'm sure you know what I had to say to them in that email). A simple problem isn't always fixed just because you buy the "NEW" part...I have learned a very valuable lesson.