|Dell don't just source their laptops from one supplier, and the manufacturer's tend to be ones that are not mainstream names. And judging by the quality of the eMachines I've seen it's highly unlikely they are Acer sourced either.|
If the emachine disk is branded as 'emachine' then it is almost certainly a recovery disk, not an oem disk, in which case it will only work with emachines. You need to get an oem disk, or possibly a retail disk, for your best chance, even an Acer one may not work unless it's for the same model range.
Unfortunately Vista is not as flexible when it comes to reinstalling as XP was so there's a very good chance of is blue-screening half way through but the only way to check is to try it, you lose nothing, just make sure you untick the box that says 'activate immediately' and don't activate until you have the basic hardware device drivers set up, otherwise you'll only need to reactivate again.
"I've always been mad, I know I've been mad, like the most of us..." Pink Floyd