I'm on Slingshot and their DNS does not work well for me at all. Had similar symptoms to what you have and I changed to OpenDNS and all problems gone. Note that I did not make the change at the modem, I think that was the problem source as I had to put the dns settings manually into each PC before normality was restored.

These are the OpenDNS servers:

 

  • 208.67.222.222
  • 208.67.220.220
If you have kids on the Internet or a business, you may want to use their services for blocking dodgy sites - http://www.opendns.com/.