2000 Tundra overheating blues...

Hello fellow Toyota enthusiasts!
Part 1: The problem... I bought my truck a little over a year ago. It had a low radiator when I bought it and after topping it off I discovered why. The upper tank was seeping and making a sticky mess. I kept an eye on the level and temp and it did not appear to be an issue just letting the level remain just below the upper plastic radiator housing. Last week I had to drive home in low range because the roads were a sheet of ice. The truck ran into the red by the time I got home. It was about 1 1/2 miles from the time I went to low. The next day I went to check out the damage. I brought the radiator back up and the coolant was pouring out of the upper part of the radiator where it was seeping.
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Part 2: The attepted repair...I put in a new radiator, refilled, and warmed to normal operating temperature while watching fluid from the filler on the radiator. I noticed the lines for the heater core cold and the lower radiator hose cold as well. I took the truck for a quick drive around the block and within a quarter mile the temp shot up and the quarter mile back and it was in the red. I let it cool down, pulled the t-stat, put it in a pan of water to boil, it did not open. Ah hah! Trip to store for new t-stat, install, fill, idle to normal operating temp for 10 minutes, same cold hoses, same overheating around the road and back.

Part 3: The solution? Should I try removing the t-stat? Cavitation issue? Can a water pump just stop pumping?? Any thoughts or ideas on what my next step might be would be appreciated!!