Even being that old, it shouldn't take so long to load. Have you checked to see what is starting up when the computer does? The more that is, the longer it will take.
In regard to the browser, you may want to clear out your history and cache. That can make it take longer and longer to load.
Lastly I would suggest doing some good deep virus and malware scans. All this should have a large impact.
And, yes, some parts can be upgraded, some really can't. However if the computer is full of stuff that is hogging up the system (mentioned above) changing components won't help much until it is cleaned up.