Now I'm over my insanity streak, here's a few more points to think about.
MS have a whole bunch of wizards that work in the background, some deal with network connections.
When you turn a Windows system on and it has a network interface card (NIC) it tries to access the network, especially if it's set for dhcp. If it fails to find a dhcp server it sets up with a default MS set up (I think it's in the 169 IP address range from memory), it's partly because of this behaviour I set up static IP in my home LAN. When you open IE it automatically tries to find the Internet, if it can't it sometimes assumes you are using a dial up instead of a direct connection. At times these two 'automatic features' conflict and cause problems, that may be the case here.
If you have both wired and wireless NICs you could be getting a kickback from the above. Especially if you use one NIC at one location and the other NIC at another.
Next time the IE doesn't work, check the Internet Options and see if you can tell which method of connection IE thinks it's using. Also, in the Command Window, run the command:
ipconfig /all
and see what it has to say about the active adaptors, ip addresses and dns settings. After noting that info try running the command
ipconfig /renew
and see if it changes any of the settings and if IE works if it does change any.