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This site's name is Get Satisfaction, so hope who administrate it does no bury this post.
What you need is Opera.
Minimum configuration for Opera:
* 20 MB of free disk space
* Any system running Windows 95 (or later)
Windows Me is a security risk too, hope at least your system has a firewall. Maybe you have a friend or know someone who can help you to upgrade your system without spending money.
Sometime ago I bookmarked the site "Windows Millennium Edition (Me) essential free upgrades + fixes", maybe it interest you.
If you search the web (Windows XP for old PCs) you can find tricks to run Windows XP on machines having low system resources.