I assume warranty is a no go?
Before rooting/downgrading a few other things to try;
1) Make a goldcard, I predict you needing one down the line...... (at the very least get the memory card CID (mmc2))
2) Try a factory restore in recovery mode ( boot into hboot > Recovery > once in recovery go vol up plus power to bring up menu)
3) If that fails then it is VERY likely a hardware fault, but if you want we can still try to root and try a different ROM.