IDK how you would lose compression that fast unless it overheated or something. Sounds like you have a few issues going on.
On the boost, that could be on your ignition system - or a vac / boost leak, it wouldnt be from the supercharger itself, more likely the IC tubes leaking.
Starts and dies .. I could check for codes to see if anything is funny, could be a Cam position sensor, ignition module, etc.
A lot more information on these supercharged cars is available on the SCCOA website.