It does seem the spyware in the restore point issue is not related to the connection problem. Was there anything else you were doing to the PC at the time? Any settings changed, programs changed, other scans going on etc? Could you have inadvertantly deleted something else? Is it possible for other programs on the computer eg AV updates, email, etc to connect? Cable, or dial up? Checked with your ISP that there isn't a network problem? Is the modem indicating connectivity? What sort of firewall is it and do you also have an antispyware program resident?
A bit more info, if you have any, might help.