Having at last succumbed to the temptation to go 'post-WWII' with a non-functioning IIa (I have managed to fix and make serviceable a coupl of Contax IIs, with sound advice from a number of RFF members) I would second everything flavio says. My IIa has responded to careful cleaning and watch-oil lubrication (not a difficult task) by all shutter speeds, from one second to 1/500th, waking up and rangefinder function restored simply by oiling the swinging-lens pivot. So far so good, but at 1/1250th the shutter runs closed. I am a great believer that assuming that settings should be left as found, on the assumption that today's problem is simply dried-out lubricants and maybe dirt/corrosion - so should I remove the whole shutter assembly and clean/lubricate further?
One NB from my limited strip-down so far: all the lens mount screws had a thin washer behind them and when an extra one dropped out on the rubber work mat (and did not bounce off onto the floor - I am learning) it was easy to establish where it had to go, as the focussing mount stiffened up on tightening up all the screws but operated normally on releasing one in particular... You have to be SO carefully stripping down these cameras.
I'd love to send it to Henry Sheerer but hell, I only paid £50/$50 for the thing...