Overheating

No pressure on one side of the radiator would indicate either a bad thermostat or a clog somewhere in the cooling system. Have you tried replacing the thermostat? Also, is the cooling fan running when it overheats?

I would just go ahead and replace it if I was you. I do it any time a car overheats because if nothing else, it is weakened by the overheating. Plus they are only about $10.00 and replacing it is a surefire way of ruling it out. And if you take it out to test it then you will probably have to buy a new gasket, and you will already have the thing out anyway.

Ok. Have you done anything with the thermostat yet? If so, and it didn't solve the problem, then we're looking at a clogged cooling system, a bad water pump, or a blown head gasket.

Head gasket test: https://www.2carpros.com/articles/head-gasket-blown-test

If it's the water pump, the problem would be that one or more impeller blades inside the pump have either bent or broken (probably bent if you're not hearing any noises). You'd only know by pulling the pump and inspecting it, maybe even comparing it to a new pump.

If your system is clogged, then water can't flow and the system overheats. Best way to test that is simply trying to run water from your water hose through it and see if it comes out the far side of the system.