Usually there's a second disc included which has the necessary drivers for your system, and maybe several others. Of course if you're trying to use a Dell disc on a Compaq or the other way around, that will naturally lead to problems.
But no, there is no way to do what you want, so my suggestion would be to go to the Dell and HP websites, download the drivers needed for each system to get you back up and going, then burn those to a CD or DVD depending on how much space you need. Then you just keep it with your restore media, and so the next time you do a restore, you already have a set of drivers that will work.
Folks my question is a bit general. If i use my Dell or Compaq re-installation cd on my PCs, i notice that some drivers are usually missing in device manager. Now! before using such CD's, is there a folder on the computer that i could copy that has all the present drivers on the pc before i wipe the hard-drive, that would make replacing the PC drivers less of a hassle. The drivers that are usually missing is Audio, Ethernet controller, VGA, etc. these DRIVERS ARE SOMETIMES A PAIN TO FIND ON Dell or compaq driver download sites.