If you don't have high confidence that your system is clean, you might use one of the bootable Antivirus scanners and also go on to carefully look around at what is started (SysInternals autoruns program is a useful tool) and how things are configured in general.
If you are familiar with Internet protocols you could snoop traffic to examine what is happening at that level (Wireshark is useful).
One way to test for some spurious network activity is to run a test client on one machine, a test server on another machine, both machines directly connected or on an isolated LAN. If that proves negative and one wants to test through their ISP, they can run the test server on a remote host (assuming they have access to one). There are numerous free network test programs including some specific to HTTP. There are also numerous perl scripts and other types of programs available as source (if you program).
If you are on a LAN with others, they can sniff the packets to/from your machine which makes it easier to pull various pranks/attacks.