My husband and I both lived in NJ and worked in NYC between Jan 08 and Sept 08. Is it true that since we were only part year residents in NJ that the credit for the tax we paid to NY is disallowed? It appears that since neither of us paid any tax to NJ throughout the year we now owe NJ a lot of taxes even though we already paid a large amount to NY. Why does being a part year resident change what taxes you can claim that were paid to another states?

No - it is not true that part-year residents can't take a credit for the taxes paid to NY. Take a look at form NJ-1040 (which is the form you should be using, even though you were a part-year resident) - Line 40 is where you take the credit for income taxes paid to other jurisdictions.