The most common problem that a bad radiator cap causes is it causes the system not to pressurize, resulting in overheating of the engine.
The radiator cap is more than just a cap and is basically a valve that has a spring that opens up when the radiator gets too much pressure in the system.
If the radiator cap doesn't open up then it can cause overheating of the engine and could cause a hose to rupture and lead to overheating of the engine.
If the radiator cap stays open and doesn't seal then the system won't pressurize and then cause the coolant to evaporate which also leads to overheating.
You need the proper pressure in your coolant system for the cooling to work properly on your engine otherwise your engine can overheat and cause engine damage.
Once that happens you likely need a new engine.