A FIX USING JUST THE HDMI CABLE:
I was having the same exact problem, but just now managed to get my brand new Mac Mini to work with my HPw2207h using just the hdmi cable. First temporarily connect the mac mini to any other monitor or TV that will work with it. Open the "display" window under System Preferences (which you can get to by clicking the apple logo in the upper left screen corner). Disconnect from the first monitor and immediately connect to the hp monitor (without of course shutting down your computer in the process). Once the hp detects the mac mini and starts doing the flickering thing, hold down the monitor's auto/select button and the "+" button right next to it with one thumb, keep them deepressed -- the screen image should actually stay solid for a second or two, hopefully long enough for you to have a good look at the display window you opened in the previous step and move the cursor with your free hand to a resolution setting other than the non-functional 1680 x 1050 setting; the one immediately below it, 1600x900 seems to work. If you loose the steady image before you do all that, just press and hold the two buttons again and try to get that cursor over a good display resolutuon, then click, wait a few seconds, and whalah, hp monitor will be colorfully filled with your mac mini output, with no flickering,
A few more thoughts: I don't think this had anything to do with my success, but before I tried all this I held down the hp's on off switch for 30-60 seconds to "reset"the monitor - something I read in another thread. Also, if you are having trouble actually seeing what resolution your cursor is on during that precious, yet brief flicker-less moment just try clicking any resolution, with the exception of 1680x1050, they all work. If you click one and nothing happens, it may just be because a dialogue box popped up with a warning about things not displaying properly if you switch resolutions, just press your keyboard's return/enter key which should hopefully register as having pressed "ok" in the dialogue box. Once you've gotten any resolution to work, you can then see enough to test the others to find the best one for you.
ONE POSSIBLE PROBLEM THOUGH: While my monitor now displays clear, vivid images at 1600x900 (and 720p and 1080p) none seem to be displaying text with the crispness I would expect -- everything is perfectly readable, just a tiny bit fuzzy (just the text not the images). Is there some sort of text setting I can adjust? Or is it just that this monitor really needs 1680x1050 settings for perfect text crispness? If so, I may still be tempted to buy the adapters described above.
