In my oppinion, the most important thing is to uninstall the IDE/S-ATA Controllers from the old windows before you connect the HDD to a new mobo.
Preinstallation has to be prepared, otherwise you have to face a completely new OS installation.
Good point Peach. In fact, for the most successful upgrade, we uninstall all hardware drivers first and revert back to what Windows is most comfortable with, its native drivers. You also have a better chance of success if you stick with the same family of chipsets and by setting the standard VGA resolution of 800X600. There is no guarantee it will work, but it minimizes the risk of failure.
Typically, one of the best tutorials for replacing a motherboard is by
TheElderGeek. As he correctly points out, often the deal breaker is the OEM disk for Windows. If you enter
replace boot drive in Google you will find a couple million hits with suggested procedures - as mentioned earlier, there are many utilities available designed for that purpose.
FTR, although upgrading an emachine is certainly possible, I generally don't recommend it. As I mentioned before, they are often described as "disposable" - just as you would not refill a butane lighter, but rather buy a new one, such is often the way with emachines. That does not mean they are bad, just not designed to be upgraded.
This is often exacerbated by the automated techniques used in the assembly process - and not just for emachines, either. For example, Dell machines often come with motherboards that are not screwed in. Rather, they are clamped down by "prongs" punched out of the sheet metal of the case. Unbending these prongs often results in them breaking off. This results in no way to secure the motherboard to the chassis at that point because there are no tapped screw holes. If several prongs break, the replacement board may not be properly secured. The end result is a new case may be required. This then can snowball into needing a new PSU, fans, floppy. Before long, you end up with a new PC anyway.
The best advice I can give is to backup any and all critical data, take all necessary steps to revert your existing system back to Windows "out-of-the-box" configuration, cross fingers, proceed carefully.
****
To the problem at hand, we still need to determine if the OEM PSU is suitable for use with a standard ATX compliant motherboard. Although nothing is better than a good multimeter in the hands of a qualified technician, a PSU tester, such as
this one from FrozenCPU give a pretty good idea of the PSU's status. If the PSU has a proprietary configuration (not good for ATX compliant ASUS boards) this will show it. I keep one of these in my tool bag at all times. CompUSA has a less expensive model
here.
****
My apologies to all for my part in the "tone" of this thread becoming unpleasant.
You are scaring me here!!! I don't understand what you did. What bothers me the most is when you said,
That's certainly not true. Just about every retail boxed harddrive comes with a utility disk that will allow you to copy your current OS installation to the new drive. And although swapping motherboards while attempting to keep the same OS installation can get ugly, with a little pre-install preparation, you can swap the motherboard out too without formatting or reinstalling Windows quite easily. 
