Now that is the way to fix a tank
My compressor pump took a dump but the tank doesn't leak. I would love to fix it with a Salor Beall unit, but for now I am running a cman oil lubed unit that is similar in output and I will plumb it to the old 60 gallon tank for more storage.
I was going to suggest looking into having the tank checked by ultrasound. There is a local place, to me, that inspects welding tanks, but I don't know if they do ultrasound or would do a compressor tank. They do propane as well.
While tank explosions don't seem common, I would not chance it with an old leaking tank. Trash it or have it professionally repaired and re-certified.
OP, was your motor and pump pretty worn as well? It seems that the pump is more likely to fail than the motor and people want stupid prices for pumps that they try to sell used, on craig's list. The working units are usually 3 phase and more often 7.5hp and bigger rather than 5hp.
It seems that a whole new compressor is the best bet, if it is in the budget. It is also easy to write off the cheaper units and talk one's self into the $1500-$2500 price range.