I had a 2003 H2. Bought it November 2002. One of the first in the city. 400 miles my front diff cracked in half. The result was because the during the casting process the diff was not cooled properly therefore making the diff crack (thats what they say). I had to pay 200.00 for towing. NOT COVERED or Reimbursed. Got the truck fixed in 2 weeks.
After that and 85,000 hard miles (offroading, going to Katrina from L.A.) numerous hummer events - over 30) My H2 was awsome!!!
Now I bought the H3 Alpha. 1700 miles. No problems.
There is such thing as a lemon. You probally should have documented your problems and spoke to a local attorney. A couple of phone calls to the GSM of the dealer by the attorney OR a call to Hummer North America seems to work wonders. That would be my suggestion.
When you bring in Hummer of N.A; things seem to get fixed quickley and correctly. Who knows, maybe this isn't the first complaint about your local dealer.