Trying to help my in laws with a 2005 Mini Cooper base with a manual transmission and the codes P0304 and p0313. Can someone direct me on where to start? I’m new so if there’s a thread that covers this, can someone please send me a link? I know misfires on these can be tough to track down. Thanks

 

Shop says it’s either a bad valve or piston ring. Coolant system holds pressure x 2 hrs without coolant leaking into any cylinders. Cylinders #1-3 have approximately 150psi, #4 has 50 psi.
I feel like I could remove the cylinder head myself, and have it repaired or put a renewed one on without too much problem, but the potential that this could all be a bad piston ring has me concerned. Is the valve much more likely or are bad rings equally likely on these cars? Thanks!