10.6. - MacPro - Sony HDTV KDL 46 XBR 4: no 1080p 50Hz/60Hz possible?

Hello!

My MacPro (MacOS X 10.6, ATI Radeon HD 4870) is connected to a Sony KDL-46XBR 4 (in Germany called Sony KDL-46-X-3000) over MiniDisplayPort-DVI-HDMI.
I can't get 1080p 50Hz (Pal) or 60Hz (NTSC) to work, the screen stays black. Only 24 Hz or interlaced resolutions seem to work.

Here an overview:
Resolution
1080i - 50 Hz (PAL): works
1080i - 60 Hz (NTSC): works
1080p - 24 Hz: works
1080p - 50 Hz (PAL): doesn't work 😟
1080p - 60 Hz (NTSC): doesn't work 😟

The manual of the TV says, that the followed resolution is understood if coming from a computer:

HDTV
Resolution: 1920 x 108 Pixel,
horizontal frequenz: 67,5 kHz
vertikal frequenz: 60 Hz.

1080p - 60 Hz should work, but doesn't.

Has anybody here any Information on how I can get it to work? Any Help is appreciated!

Greetings from Germany,
Matthias