Even more surprising, in my remote village where the analogue signal is so poor and provided I only have an indoor antenna, the digital signal strength was strong enough, about 90%!
The only problem was that I only had sound, as well as a "HD Service" pop up message on screen.
These two symptoms required two distinct solutions:
Sound but no picture: In current TV's most tuners are MPEG2 only, and, unlike the rest of Europe, Ireland adopted MPEG4. By chance, my monitor came with a CAM slot, so I ordered a CAM that enabled the conversion of MPEG4 stream, bringing a clear picture for every channels. At the price of 60€, one may decide to wait for the specifications of Irish TV to be finalized and buy a complete decoder unit for about the same price.
"HD Service": With the appropriate CAM inserted, I expected the bouncing "HD Service" text to disappear, especially with unencrypted test channels. Unfortunately, most LG TV's came with a bug that requires a firmware upgrade (anything above v.3.51.01). Greeks and Polish forums are well aware of this and some even provide links to the firmware files, but not for my model. Too bad! because all it takes is to store the firmware on a flash drive and plug it in the USB port marked "service only". With the "Software Upgrade" option enabled, this update is being loaded automatically.
I've tried the LG support, and they arranged a return to a service centre. I joined the firmware upgrade details just in case, although they're supposed to know better. well, they sat on the monitor for two weeks and returned it with a reply like "There's not fault in the monitor, check your TV signal...". They later confirmed that they were unable to obtain the firmware.
That's official, the LG support in Ireland is hopeless. I hope I'll never have troubles with my BD390 now.
Update (October 2012): Firmware resolving the HD Service message
Just put the file in the root of a flash drive and turn on your monitor, a "TV Software Upgrade" message will follow. Tested on LG M2294D-PZ. If it doesn't work, try with another flash drive.