Hi, I have an intel Mac Mini 1.66GHz core duo and a Sharp 26" LC TV HD dvi to hdmi and had display trouble at initial setup. What I had discovered was when the mini had been using a vga display originally and then switch to this display, at boot the system created display over-rides in System>Library>Displays>Overrides
Here is what to do:
You need to connect the mini to a VGA display temporarily to do these modifications.
Go to System>Library>Displays>Overrides
Find out which over-ride has been created most recently by the modification date, and delete that one by moving to the trash and then shutdown the mini.
Resetting the PMU
Unplug all cables from the computer, including the power cord.
Wait 10 seconds.
Plug in the power cord while simultaneously pressing and holding the power button on the back of the computer.
Let go of the power button.
Press the power button once more to start up your Mac mini.
Important: This procedure also resets the computer's PRAM. Be sure to reset your computer's time, date, and other system parameter settings as
necessary.
Once the Mini reboots re-connect the dvi-hdmi to the mini making sure the display is off but the hdmi end is in the tv's hdmi port. Turn on the display and you should now have the display working at 800x600, which is default for non Apple LCDs. Re-connect the keyboard and mouse and open Display Pref.
Your display and the Mac Mini will both handle 800x600,1280x720 and 1920x1080 all 60Hz and the display prefs will allow others but be sure never to use them, as the Mini will support them but the display will not.
When detecting display button is pressed mine is detected as Orion LCD TV/Display and even System Profiler confirms this. Not sure which if any yours will detect.
One other note, because you are using a 26" and the max size display any single port dvi Mac will handle is a 23" you will have a 1.5" black border around our Macs desktop. On some LC TV's the display is scaled and you cannot see the menu bar. To fix this go to Display prefs >Options and click Over-scan to turn on and then once again to turn back off and it will not be scaled, you should now have the entire display and a beautiful picture.
By the way, the DVI to S-Video solution is horrible on LCD TVs. The fonts are distorted and the images are faded.
Good Luck!