Sunrise may be the brightest time of the morning...but the user using that name should probably call himself "Lunar Eclipse in an Unlit Coal Mine", because he's about that dim.
Emptying your Temp Files folder will actually SLOW your ability to surf the web, since the pre-loaded info for the sites you regularly go to is stored there.
See if you have access to high speed via a cable modem with your local cable TV provider. Other than that, you can try to investigate the possiblity of Satellite Broadband. It does have some significant drawbacks, but none of them make the use of the service untennable. As one poster mentioned, bad weather can jam your service partly, or completely, and for a few minutes a day over a couple days twice a year you will have NO service as your antenna stares directly at the sun instead if the satellite.
As for loading faster over your existing service, there are any number of programs that promise faster downloads and page openings. How well they work, I honestly don't know, as even when I was using a 56kb modem, I never bothered trying any of them...(mind, I was only seeing 28.8 to 36 something connect speed, despite the fact I was less than a block from the main switch.)
The "best" way to speed-up page loads is to not wander too far from the pages you always go to. Short of that, close any competing processes, and make sure your PC's memory exceeds the recommended memory. In otherwords, if you're trying to load a webpage and using an IM program at the same time, the page is going to take forever to load.
Now...to deal with the next bit of inanity... Buying a NEWER computer and connecting it to the same 36kb connection will do absolutely NOTHING to solve your "problems," so ignore everyone telling you that this will solve your problem.
Theoretically, you can increase the speed of your dial-up connection quite drastically by using specialised connection that involved two side-by-side phone jacks. It ain't cheap, but in areas where you don't have DSL accessable, it could be the way to go. Please note that the specialised modem and the second phone line will be a pretty penny each. Some telcos will even have you paying for a second line, since that is essentially what it is. It also mimics a DSL connection in another way too...you can make and receive calls while you're on-line.
Good luck!