Um... NO!
A Retail CD has different "special files" as opposed to an OEM Install. The COA Key will not work on a Retail CD.
Hint - search for OEMBIOS and SETUPP (particularly on the Dell HDD). You can Google that along with "site:msfn.org" (no quotes) for some helpful information. You will NEED those to create a Dell OEM CD (useable with the COA key).
In addition, you will STILL have issues with the SATA Drivers that will NOT be present on the CD, the only work-around being Disabling SATA (AHCI) Mode in the Atom PC's BIOS -OR- Integrating the CORRECT SATA Drivers for the Atom PC into it (see HINT above).
It's NOT just "slap in in and Repair" or "just swap/clone the HDD to another PC". Not that simple. It probably WILL NOT BOOT (blue screen).
BTW, it will violate the EULA to use that COA Key on another PC. They (any Retail/Upgrade/OEM) can be used ONLY ONCE on a given PC and it WILL need activated. The COA Key is assigned at the Factory to that PC even though, by manipulation, it can be used on another.
I can't won't give any more on this so do your own research (via google on above). The subject is all over MSFN as to the Exact Differences between All Editions/Variations in DETAIL (keys, files, etc) as well as the WWW, so think first before you act.
Side issues -
Is the OLD PC that bad or is it just loaded with "garbage" or Trojans/Viruses? If either/both is true, then even transferring to the Atom PC won't help and a good "cleaning" would make it all good again . Don't be so reluctant to give Make/Model of both if you want further help.
HTH and good luck! I've said almost too much so I'm done...
This post has been edited by submix8c: 31 January 2013 - 09:53 AM