Hi Clueless,
Hopefully you have an antivirus program already running on your system when you go and get these downloads. If not, use another computer to get these files and transfer them to your computer while not connected to the Internet.
If you do not have an antivirus program installed, do not put your system online until you have one installed.
SingularLabs has uninstall programs for most, if not all, major antivirus vendors: http://singularlabs.com/uninstallers/security-software/
Run the uninstall for all prior versions of any antivirus you have ever had on this system. Check with the previous owner for prior history if you can.
Avast! removal tool here: http://www.avast.com/uninstall-utility Avast aswclear.exe must be run in safe mode only and the removal tool must be placed on the desktop only.
Remove all older versions beginning with the newest and work your way backwards. Reboot after each uninstall.
NOTE: Be sure you are only removing Avast! software and folders/files and nothing else with this tool. To ensure this is so, place this tool on the desktop. Very important. (See step # 1 on the aswclear.exe webpage) Read this entire page until you understand it.
Once the left-over remnants of all previous antiviruses are removed, then you should be able to install Avast! Free version 7.0.1466, which is the latest version available. You can get that here: http://www.filehippo.com/download_avast_antivirus/ Once that installs successfully, you should be able to go online, provided your firewall is turned on.
It is likely old left over files from prior uninstalls is causing your problems.
If you do not want the browser, Google Chrome, to install with Avast 7.0.1466, be sure to use the Optional (expert) installation page, and untick Chrome install.
EDIT: Windows 2000 must be updated to Service Pack 4 for this to work. (Microsoft Rollup Package)
Here: http://www.microsoft.com/en-us/download/details.aspx?id=18997