How new is the battery? Could try jump starting it from another car to see if boosting the battery power helps.
Go back to the beginning and get someone else to oversee you testing each component. Don't assume just because its new, its working properly - for example, batteries are known to not have a great shelf life and if allowed to become flat, for months, sitting on a shelf, can be ruined. So, test EVERYTHING, if you can't test it yourself, get someone else to, a garage if needs be.
All of this sounds very similar to my problems which I've had for years now but being poor and the car starting eventually I tend to ignore it...however I left the stereo on for 12 hours the other day accidental then came to start the car a fortnight later...and it turned over even more pathetically than usual. Connected up my 1.1i Saxo and it's itty-bitty battery and the Golf started much easier than usual, so a new battery is on the cards for me when I have some green. Anyway, just try jumping it from cold from another car, I'm sure a neighbour/friend will oblige, and see if it helps...it's a free test and you have nothing to lose, I'd offer myself but Bristol's a bit of a trek from Soton! Oh, and did you say you measured 12.2V across the battery...that's not great...mine's pretty dire at starting my Golf and it reads about 12.2 too when the car is off and only 13.2 when running, compared to my Saxo which is 14.4 when running about about 13.5 when off, so again, new battery time...doesn't matter if it is new, if it's been drained then not trickle charged or stored for a few months then it can still be ****e.
Hi Slowly discharge the battery, then charge it up slowly. That will revive the battery. Then replace the brushes/voltage regulator on alternator on the Golf.
