How to make old pc run faster?

My grandparents have an old HP Pavilion a1129n from 2005 and is running Windows XP SP2. Over the last year or two its been slow. I'm good with computers and I'm good at optimizing them but I can't get this thing to run any faster. It has a slow start up about 2 to 3 minutes. Slow in general like only being to run one or two things at once but it can do that very well either. After its running it constantly slows down until it starts to freeze then you have to restart it. I did a factor restore, put my own firewall on it, put malwarebytes on it, and ccleaner on it. ran them all but it still has only a little improvement. I know it ran faster when we first got it and should run fine with the OS it has on it because I have fix and used older machines at my school and they run as good as my main computer. I'm starting to think its hardware like the RAM is malfunctioning. I got a tip from my school system administrator and he said to get a pencil, take out the RAM, and rub the contacts with the eraser of the pencil because they get some type of gel on them and have done this to computers at school and it work. I still want options of some other people on what to do to this machine. Can anyone help?