Hardheaded User...
I don't envy you. I had a similar user with exactly the same complaint, her computer was never fast enough. Nothing I did solved her problem until I realized one day that she was simply wanting attention, and having limited understanding of computers, the speed was all she understood to complain about. In the end, I managed to quell her constant cries for help by putting her in charge of the toner cartridges - believe it or not. I asked her to check the status of the toner cartridge in every printer every day. I even created a small spreadsheet for her to fill out with the status of each cartridge and send it to the IT department. Although it still meant that I had to spend a minute or two each day reviewing her report and giving her a response, it was a more pleasant way of interracting than listening to the constant complaints I could do nothing about. She never complained about the speed of her computer again. I'm not saying that this will work in your case, but sometimesit can be useful to try to consider whether the user has an underlying motivation even they may not be aware of. Good luck!