You're right - both of your alternates are better. You can visit a website, but not the Internet as a whole. It definitely doesn't work if you're also trying to tell people not to use any internet functions, such as email, messaging services, Skype, etc.
The sentence 'browse the internet' would probably be taken as specific to the web - and not relate to email and other services either. So, if you want to stop people using the internet at all on XP machines, I'd use:
Don't use the internet on Windows XP machines.
If it's just the web you're talking about, try:
Don't browse the web on Windows XP machines.