To answer your question regarding the hard drive more directly, no, It will not work. Hard drives are, unfortunately, not plug and play. When you change the motherboard, ect, or put it in another computer, there are driver related issues that prevent it from booting. Again, I had your same problem with the same computer. Again, I tried all of the things you tried and a few more. Including all of the suggestions that have been made here so far. To prove the point, I even tried to put the hdd in an dell 2400 P4 i had laying around and could not get it to boot until I cloned the original Dell hard drive. The problem is on the motherboard. There's not much you can do about it...
Except prehaps buy a new motherboard. Now I looked into this too and there are a few problems with that idea and this computer. 1) It's hard to find a micro-atx board woth the trouble. The selection in comparison to atx or other formats is very limited. 2) As I mentioned before, this case is not well ventialted. Installing enough fans (the originals are 80mm) will be almost impossible, short of breaking out a hacksaw. 3) you would need a much more powerful power supply and I had a heck of a time fitting just a 350w in that case.
Basiclly the case is not a kit case and is not worth messing around with. If I were you and you wanted to go the DIY route, I would buy a new atx case and recycle as many parts as possible from the a720n. Although, you will not really find a place for the AGP video card or the ddr memory is any new computer, as tech standards have changed considerably in 5 years. I have nothing from my old computer in my new one except the dvd drive. Then , you'll want Windows 7 or Vista, which you don't have at the moment and doesn't come with any kit. Consequently, in the end, you'll wind up paying as much for the DIY than a good mid level quad core ($600 ish). I picked up a HP Pavillion p6720y with an AMD Phenom? X4 9550 quad-core processor and 6GB DDR2 SDRAM for about $600. For a few bucks more, you can get the HP p6130y with a better cpu and more memory. And if you buy any computer now, you get the free Windows 7 upgrade in a few months. Either way, if the a720n is your current computer, you'll not be dissappointed. And you may even save yourself a few bucks buying out of the box.
Let me know what you decide.