Does this set have any internal test patterns? And if so which part of the service menu are they under?

I've been searching for the past 45 minutes and haven't been able to find a thing, either on Google or AVS.

No. Use a DVD for test patterns. Avia "Guide to Home Theater" should have enough patterns for you.

I believe the internal test patterns are generated in the Q-box assembly. The Q-box is associated with the ATSC tuner. So, no ATSC tuner; then no Q-box and no internal test patterns.