1995 Pontiac Firebird Radiator Circulation

About 6 months ago, my car started to indicate an overheating condition. I stopped driving it and saved up to fix whatever the problem might be. I took it to get the radiator flushed about 4 months ago and still nothing. I haven't driven the car other than that trip until 2 months ago when I had a new water pump, coolant sensor, and thermostat installed, when that didn't work, I parked it again. The temperature gauge gets up to 260 degrees pretty fast on the panel and the low coolant light is always on. If I let it sit for a few weeks, it looses some coolant, but not much and I can't find a leak anywhere. Yesterday I popped open the hood and tried again. I start the car, let it idle and watch the gauge go up. The coolant stays cold, and doesn't appear to be moving. I thought it could be the head gasket, but I have no white smoke, no oil in the coolant and no coolant in the oil, nothing. Usually the car would cool off at highway speeds, but when I got into town, it heats up. Both fans appear to be working. I have noticed that inside the radiator is very rusty. When the car is at 250 degrees, one hose is kind of warm and the other hose is still cold. There's no pressure on the radiator cap, the overflow hole at the top of the radiator was clogged with what appeared to be rust so I cleared it. The cap has a slight crack in the rubber, but the spring works easily. The hoses are a little soft, but look like they're in decent shape. I'm at the end of my rope and could really use some expert advice. Please help!