I picked up a 2002 fullsize XLS with 3.5 L, 180,000 miles. Owner said it had a bad head gasket and had minorly overheated once or twice as he drove it home. I confirmed there is water in the oil, and some missing radiator coolant. He installed a new radiator but that didn't fix overheat problem.

It wouldn't crank for 3 days and then yesterday it started up. Very rough and seems to be placing a lot of unburnt fuel out tailpipe. Not smoking very badly at all, just sounds and smells very fuel rich. Very little faint white smoke, which I hope means the head gasket break is very small.

Ran the code reader and it shows P0300, Multiple Cylinder Misfires Present.

My friend thinks a bad fuel injector may have blown the head gasket. Is that true? If so, I want to check them all over.

Do these injectors commonly fail and cause damage to themselves?

Has anyone has success at checking and bench cleaning the injectors like the YouTube videos describe?

After I check injectors I plan on changing motor oil/filter with 15w-40. Then draining, flushing and backflushing radiator and heater core. And finally adding a bottle of Steel Seal to see if I can solve head gasket leak that way, without pulling heads off.

Any suggestions on what to check other than injectors, for the bad head gasket cause? I don't want to repair it just to have it break again if I can avoid that. Thank you!