I just built a gaming rig based on the DQ57TM mobo with a first gen i7 860 and am experiencing the EXACT same issue as the original post. The previous "answer" failed for me, holding down the power button until the machine shuts off then trying to boot again did not work. I fail to see how it would, since holding power button tells the mobo to power down, but I guess there may be something built into this mobo's architecture that disconnects power from different parts of the mobo at different times resulting in successfull subsequent start-ups.
However, the GOOD news is that I have found a fix. Powering down the machine (whichever way floats your boat), unplugging the power cord, removing the cmos jumper from pins 1-2 and placing that jumper on pins 1-2 on the pins directly above the cmos pins for 5 seconds or so, then replacing the cmos jumper back where it was. This clears the cmos settings. This seems to be working reliably for me. For more details on clearing cmos settings on this mobo see page 62 of this document:https://downloadmirror.intel.com/18507/eng/DQ57TM_ProductGuide02_English.pdf
Also, FYI, in my search for answers I read that this mobo is unable to use RAM with operating voltages above 1.6v. I haven't tested as all I currently have are 1.5v sticks.
Also, I have what appears to be the most current BIOS version TMIBX10H.86A 0050. I wonder if there is a setting in the BIOS that can stop this issue, it's really annoying needing to open up my machine every time a hard shut down occurs.
UPDATE: I just downgraded my BIOS version to 0025 and the problem no longer persists. I cant help but wonder what other problems with my setup might be unaddressed now, but at least I dont have to clear the cmos every time I experience a hard shutdown with this machine. Oh, and now the machine chirps 2-3 times 6 seconds apart during power up. I have no clue what that means. I did try all of the BIOS options, the OLDEST one Intel has on their downloads page is the ONLY one that works. Maybe they will fix it with a new BIOS, but I won't get my hopes up, the current latest version ending in 0050 was released in 2011...anywho, hope this helps some of you! This was definitely one of the more bizarre mobo issues I have experienced.