|I'm assuming it generally runs slowly (not just on the Internet).|
Check it for viruses - MalwareBytes freebie would be a good start:
This is simply run on demand but you also need a proper AV, such as Avast free which would be fine. Don't have two AV's permanently running at the same time.
CCleaner would help clear some unwanted junk out of the system:
Type msconfig in the run box then look in Startup. There could be some unwanted background programs starting up which could be unchecked.
Go to Device Manager (devmgmt.msc in the Run box) and if there is an option to use write caching then it would run faster if selected. There is a slight risk of data loss due to power failure but I have been using it for years and never run into any difficulty.
Might be worth running defrag too as it could be in a good old mess.
Always pop back and let us know the outcome - thanks