I want to leave this post here for the many folks, on several OS's and various platforms, having issues getting HDMI-out working with HD LCD/LED/OLED monitors/HDTV's.
For one reason or another, it was a tough subject to web-search on but eventually I found numbers of fellow travelers who had the "bug" - unable to hookup external monitors to Intel embedded graphics on core i3/i5/i-whatever.

My test mule was a dell inspiron 1121 with i3 330um, intel hd.
In a nutshell, sparing you a lot of detailed debug/root-cause and some near shouting matches with Dell et al:
- The issue is intel's fault. Poor implementation of HDCP in the chipset, resulting in very iffy synchronization that is monitor-specific, and sensitive to OEM's implementation of HotKey mode-switching. Still an issue in the latest from Intel.
- Small things can make it better or worse
- It can be solved for some monitors on some [I would say the majority] of notebooks/laptops
- To be sure everything is as late as possible, uninstall the Display Adapter using Windows Device Manager, and watch carefully on reboot to see that the MS generic VGA driver is used. I guess to be pure OCD one would want to go through the windows system files and make sure no remnant of the OEM [dell/hp/lenovo/etal] drivers are available.
- Having downloaded from Intel the latest build for Windows 8 [in our case] or Windows 7 [8 was just formally published], Use Device manager to Update Driver and point it to the "Graphics" folder wherein are the required driver files. Windows will do the work from there. Reboot.
- The tricky part then is to turn the monitor on and set the source for the monitor to the proper HDMI port you have the notebook plugged into. Some monitor implementations immediately check for signal which means not just signal but Sync [i.e. the error file is monolithic: it reports "no signal" when it gets no sync] and upon "no sync" revert to whatever the last working Source is/was. Its a p-poor way to implement in my view. Other displays do it the right way which is to hard set the mode and simply wait interminably. Hit the hotkey on your notebook to flip the mode to external - "pure" external mode is less complicated than dual-screen or extended.
If the display does not immediately appear, power cycle the monitor. It should then reset and resync, hopefully successfully if the cable/connection is good.

It is sad to see unresolved posts on this issue on OEM/vendor forums and on Intel's on community boards.

needless to say, I love ATI. This whole process is so easy it spoils one, from humble C-series notebooks through the high end of ATI dedicated, as long as the notebook mftr doesn't interfere somehow.