I have a 2007 Nissan Quest that won't start and has a P0744. Can a P0744 truly cause it to not start? It turns over but that is it.

Yes.

However, you can also have an amperage issue. Hook it up as if jump starting and try.

If you still have a no-start condition, a few possible causes:

Ambient temperature low (bring it in the garage overnight)
Fluid low or dirty
Torque converter clutch solenoid valve has failed

Unfortunately, if none of the above apply, it's likely you'll be looking at a trans replacement.