Compression in radiator

It just got a re-machined head and a new head gasket, but the mechanic that did this said the valves are going and the piston sleeves could also probably use replacement.

I don't have any white smoke, but it appears someone may have used some stop leak on it in the past.

Can bad valves cause compression in the radiator? Or is it more likely I have a cracked block (yikes!)?

The valve cannot cause any loss of compression into the cooling system unless there were a cracked block in or around the exhaust valve ports and this is very unlikely on the N engine. I have personally never seen a cracked block except from being froozen.

However, do check back with your mechanic, for I suspect you may be misunderstanding him. I really don't think he was surprised to find pressure in the radiator, as that's perfectly normal. What he may have found is combustion chamber pressure in there, as from a blown head gasket.

The head gasket isn't installed any better then the mechanic who installed it. Improper torque can cause leaks, especially with dirty threads on the studs. Then the wrench shows a proper reading, but the nuts might not even be touching the head. Using the wrong sealing materials or damaging the the head gasket can also cause it to leak.

Not saying any of those things have ocurred, but you need to be aware of them and consider the need for investigation. Engines get built wrong all the time, just look at the number of new engines that need to be replaced as a result.