That brand doesn't matter- Monster cables fail just as often as regular cables. The green tint is caused by the red cable not sending any signal.
Instead, try this- locate the Red,White and Yellow jacks on the box.
You're going to take the cables and connect them as follows:
Red Cable- into Red under "Video 1" on the TV.
Other Red into Red on cable box.
Green cable into Yellow under Video 1 on TV.
Other end of green cable into yellow on cable box.
Blue cable into white under Video 1 on TV.
Other end of blue into white on cable box.
Use Sony remote's TV/Video button to select Video 1.
Let me know what happens.