HDMI TV won't get signal

I’ve had my BBxM rev C1 for about a full year now. I got a new 1080p TV and for some reason it doesn’t accept ANY resolution I specify - it says the resolution is unsupported, which it isn’t. Such resolutions could be something like 640x480MR-16@60, hd720, 1280x720MR-24@60, 1920x1080MR-24@60 and so on. I have tried other devices with the TV at multiple resolutions and color depths and they all seem to work. One of those devices was a PC using an nvidia 7900GT (a 7 year old GPU) which I connected using a DVI-A to HDMI converter, so I don’t think this has anything to do with my TV being incapable of handling a different signal protocol.

I tried my BB on a regular PC monitor with a DVI port and it works fine at varying resolutions. While connected to the new TV, I am able to login through SSH.

As a side note, I can get s-video to work on the TV, but I don’t want to be stuck with a limited resolution and a cut-off image. Also, as soon as X starts I lose my s-video signal; it seems to switch to DVI.

Sorry I meant to say DVI-I, not DVI-A. Anyways, I installed x11vnc to see if the display is in fact working (it is) and after checking the display settings in XFCE, it says the refresh rate is 58Hz. With it saying that, it isn’t really a surprise to me that the TV claims incompatibility, but I’m not sure why it says 58 when I specified 60. If I set it to 61 or 62, the display settings reports it being at 62. If I set it to 60.0, it changes the resolution to 640x400@71.

Any way to get this to operate at exactly 60Hz?