I have a dial-up connection. I never had a problem until recently. I suspect adware or other similar culprit.
When you have the problem again, before rebooting, open a command prompt and type:
ping www.freerepublic.com
You should get something like:
Pinging www.freerepublic.com [209.157.64.201] with 32 bytes of data:
Reply from 209.157.64.201: bytes=32 time=209ms TTL=43
If you see the number like 209.157.64.201, that's www.freerepublic.com resolved to an IP address (which is what the Internet works with internally). If you get errors, then there is some issue with it re-establishing the DNS server.
If you get the IP address back and replies, you are online and it is some issue with IE.
In addition to what I described in my previous post about deleting all of the objects from View Objects in IE, look in Add/Remove Programs for something called "New.Net". If you see that, remove it. That's something that comes along as baggage with other programs or sites trick you into downloading - it is supposed to be some "new" way to resolve names to IP addresses, but is basically spyware (or junkware or whatever).
Of course, also take the standard routes - download and run Adaware (www.lavasoftusa.com), Spybot Search and Destroy, Microsoft AntiSpyware, and CWShredder. Be sure to get the latest signatures for each before scanning.
If that doesn't help, try the suggestions here.