If it is only slow online then the problem could lie with your ISP and not the computer. Have you checked with them?
An 18GB hard drive with only 7 GB free means it is more than half full. If you have a lot of music, videos, photos stored on the computer getting rid of some of those might help.
To check Java version you can either go to Start, Control Panel, Java and opening that icon will show the version number.
Also look in Start, Control Panel, Add/Remove and see what and how many versions of Java show there. Old ones can be uninstalled. To get the newest version go to Sun Java Download
Download the offline install and save it to the desktop.
Close out the browser once the download is complete. Then go to Add/Remove and uninstall all older versions.
Once those are uninstalled then double click the downloaded new version and install. Once the install is complete then go to Verify
to verify the installation was correct and complete.
IE7 has higher security settings than previous versions. This could also slow things down. You might lower these settings by going to Internet Explorer, Tools, Internet Options, Security and put the setting for Internet at Medium.
If you find the computer slowness is caused by IE 7 you might try using a different browser...I use Firefox and it is much more secure and frankly I feel much faster than IE7.