Question : can ping by ip, and by name, but not browse

Have an odd problem. I lost my main DC, so I had to promote another. Not a problem, but now I am having a weird problem with a handful of my computer.  They will not run the logon scripts, and it appears it's because they can't see either domain controller on the network.

Now, in a command prompt I can ping them by ip address, I can ping them by name, but if I go start/run \\servername it tells me either the network path was not found, or sometimes the "no network provider" error.

I'm at a loss--any help would be appreciated

Answer : can ping by ip, and by name, but not browse

Does this happen on every client or is it just one client that is having this issue.  If you switch up the DNS servers on the client does it make a difference?