Press 'Ctrl-Alt-Del' together and click the link to start it, then view the 'processes' tab. It might be a good idea to use the 'view' menu to add 'I/O' columns because it could be that some sort of regular disk access is causing the spikes.
You mention there's not anti-virus - I assume you've not connected this machine to the internet at all in order to prevent infection (it could be a virus causing the issue).
And finally, there may be anti-malware running. Although you may not have installed any, Windows 7 comes with it's own inbuilt protection. Check the 'Windows Defender' options in control panel.