We have had an odd problem recently with some change BT seems to have made with our broadand connection. The router log was showing the router was having to restart some 30-40 times a day. Our router vendor has given us a beta version of some new firmware for the router that has solved the problem.
From experience Firefox is always slower when my PC has resumed from standby, so I now close Firefox before I put my PC on standby.
If your PC is crawling along on non internet applications. Open the processes tab of Task Manager click on the CPU column twice so the high CPU usage applications are at the top. The one consistently at the top (apart from System Idle Process) could well be you offender.