The ping showing 4 packets sent 4 received non lost tells me that you have internet access.
Eh?
Answer from 10.0.0.138: Goalhost can not be reached.
The default gateway (or next hop router) is simply saying that it does not know how to reach a foreign network or host - i.e. has no route defined, or the destination network or host does not exist.
Interestingly,
www.bbc.co.uk should resolve to
www.bbc.net.uk [212.58.253.74] - at least it does so in the UK.
Juud, please run ipconfig /all from a CMD session and post the result here.
There are still several possibilities as to what the problem is - and it is probably a network problem, rather than a virus problem or an IE problem!
SD