If your rad cap failed it may have allowed too much pressure to build up in your cooling system and that cracked the rad. Now that you have no pressure in the cooling system it will overheat even of it is full because doesn't have enough pressure in the system. I would replace the rad, cap and coolant.
If you do not know when the water pump or thermostat was changed I personally would add them to the list of parts to replace. Then you might as well look at your belts and hoses also.
The 'might as wells' can get expensive....
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Getting older, I have developed some special skills. I have the ability to cough, sneeze, fart and pee at the same time.
"If we cannot afford to take care of Veterans, then we should stop making them."
David C. Wilker Jr. USAF (RET)