Lubelaczek,
Yeah, the XBR4 recognizes the 4250HD as an HDMI Device. Try a different jack on the back of the TV, if that doesn't work, try swapping the box at Cablevision. HDMI jacks on all devices are notoriously weak and break easily. If that doesn't work, try borrowing an HDMI cable from a friend that you know works to rule out any issues with the HDMI wire.
Regarding HDMI 1.3 and 1.2, the main difference is the amount of bandwidth is supports. HDMI 1.3 is really only required for Blue-Ray.
HDTV is only 60 hz, so their is no benefit of having a 1.3 cable box over a 1.2 cable box, since the TV will have have to up-convert the signal to 120 hz.
Also, all HDMI devices have to backwards compatible, so a 1.3 will be able to speak with a 1.2.
Regarding, the HDMI Cable 1.2 and 1.3 are exactly the same, except 1.3 is insulated better, so in theory it should support faster connections up to 10.2 Gbps for 1.3 versus 2.23 Gbps for Cable TV, so the wire you have is exactly the same, but just supports up to a faster speed.
If that doesn't work, check the Sony.com site to see if there is an updated firmware patch for the XBR4