Don't throw it out of the window you have a better then average system mainboard. You might have to strip the thing down to just the mainboard remove the bois battery before you remove the mainboard from the case.
What I would do is to take the mainboard out let me say. Then I would inspect the mainboard for loose connections of the mainboard heatsink to the board. If the mainboard heatsink is firmly on there then I would(because the mainboard is out of the case). Get a small screwdriver and remove the mainboard heatsink anyway. Put new thermal compound on the heatsink area's that go to the northbridge, southbridge. and check to see if the thermal blanket over the voltage regulators is not worn away. Also while heatsink is off the mainboard(mainboard heatsink I speak of) check for smoothness attempt to straighten by hand if not. With the new thermal compound on the heatsink attach back on mainboard, but before you do buy some thermal blanketing cut a small square the size of the southbridge computer chip then cut a little square hole in the square piece of thermal blanketing that you cut. the little square hole in the middle should be the size of the little square heatplate on top of the chip. This is done to ensure that the transistors and whatnot on top of the chip are unaffected by the metal from the heatsink. Do the same procedure for the northbridge.
Once I would have put the mainboard heatsink back on the mainboard being carful not to overtighten(just enough to snug it down. Then I would turn my attention to the case. Most older cases did not line up perfect with mainboards even if they are atx form factor ready. I would check the standoff screws(what the mainboard sits on. Make sure they line up with the holes on the mainboard. If any standoff does not line up perfect remove the standoff. In the end you only need four stand off screws. Then put the screw in the mainboard which drive into the stand offs. If any standoff is stripped then discard the stand off.
Put the bois battery back in then all the other stuff.
The reason I gave you all that info is because you said it try to boot meaning that something is shown on the monitor screen which tells me it is very much alive. But due to southbridge overheating on alot of older mainboard lga775 mainboards you could bring it back to life(that only if you visually see something on your computer monitor that shows computer booting process. If you do take any of this info into consideration remember(ALWAYS REMOVE THE BOIS BATTERY BEFORE YOU WORK ON YOUR MAINBOARD).