If you have double checked the connections on the splitters and diplexers, then it is either faulty equipment (splitters, diplexers, cabling), and too many breaks in the line.
TV2 signal is Analog.... so unfortunately it is very sensitive to dB loss. My guess is your problem comes down to a combination of too many breaks in the cabling (barrels,wall plates, splitters, etc.) and too much cabling.
I bet if you were to replace your wall cabling with some jumpers running down your hallways to test, you would get a great picture. (duplicating the current setup)
Keep in mind that every break in the line will cause dB loss, as well as simply having longer cable runs... as well as bends in the cable, staples pinching the line (common in prewired homes)