Sounds like a modeline issue that could be sorted with some effort. Their verdict seems like a desperate cop-out to me, especially after it took them 4 hours to figure out.
I'd say add the TVs to the wiki and put the official Sharp party line in there. That could at least save another poor soul 4 hours on the phone with them. And if you find suitable modelines lateron you can post them there too.
I don't think it's an LMCE problem because the flashing occurs at boot. Boot splash, BIOS, Post, etc.
I am using hdmi - hdmi from my abit anm2hd to sharp aquos 42 Lc64du at 1080p and its working fine.
Yeah, HDMI>HDMI works fine, problem is that the Asus b202 doesn't have HDMI, only DVI
It might be worth noting that I had problems with a blank screen using DVI->HDMI adapter with a Pioneer LX-5080 as well. Using a different adapter helped to sort things out (the original ATI adapter worked fine.)
I thought it might be the cable at first as well, I tried two different cables (Belkin and Radio Shack), both with the same results on the Sharp and both worked fine on other TV brands.