Dns Suffix?

Hi; here's a new one, bought a slightly used computer last week and it's DNS suffix was different than my old one,(of course), but here's the thing, been having all kinds of problems connecting to the internet,(lucky i'm on here now) so I hooked up my old computer and Guess What? It's now showing the same DNS suffix as the one I just bought!! Is there any way I can change the DNS suffix back to the origonal? Thanks, Roy.