If you need access to your Windows, Mac, or Linux computer from an Android, iPhone, or iPad mobile device you can use the free program TeamViewer. TeamViewer lets you access any of your computers which have the host application installed, from any computer or device running the client app. They also have a flash-based option you can use by logging in to their website.
Often the first thing someone will tell you when you mention that your computer is running slowly is that you need more RAM. While this may be a true statement, it is a good idea to verify for yourself before making a purchase.
Begin by actually using your computer. Open any programs you use frequently and might typically be running at the same time; maybe even open an Explorer window or two for a little extra. If you play a lot of games you might want to start a game and then Alt+Tab out.