Notice the "HW: 180" on this line of the cgminer output:
This indicates that you're getting quite a lot of hardware errors which is what the "invalid nonce" errors are about. There are three things that generally cause hardware errors:
1. Incorrect thread-concurrency setting. If your thread-concurrency is set too high or too low, hardware errors can result. Solution: Find your GPU here: https://github.com/litecoin-project/litecoin/wiki/Mining-hardware-comparison and adopt a thread-concurrency that is known to work.
2. The GPU is overclocked or undervolted too much. Solution: Reset your card back to default clockspeeds and voltages; use this as a starting point.
3. The GPU is damaged or defective (unlikely). Solution: RMA the card or order a replacement
My best guess is that your thread-concurrency is simply set to an incorrect value. Seek out some good cgminer settings for your particular GPU at the github page linked above.
This is a bit of a shot in the dark but if you're getting the error that I think you might be getting you need to run this command before starting cgminer:
or, on Linux:
Hopefully you can get up and running as soon as possible, good luck!