Hello, I've got an old underpowered laptop that came with Win ME, but I want to install a version of Linux that'll work with it. It's got an AMD K6-III processor & just 60MB of RAM. Hardly a supercomputer.
What I'm looking for is a Linux distro that'll work with such an underpowered machine *and* a mobile broadband dongle that'll work with it as well.
Sorting out the former is relatively easy.
Sorting out both, not so much.
Can anyone advise me?
Thank you.

You absolutely need to upgrade the memory in this machine if you want to run a modern browser (Chrome, Firefox), as just the browser alone will consume at least 100 MB of RAM performing basic tasks. The single tab I am writing this response in on Chrome is consuming over 70 MB of RAM, and that doesn't include the memory used by the browser itself and the other tabs.

Beyond that, a light distribution like Slackware, Arch, or Debian should be able to run the system and X (though with a minimal display environment) within that little RAM...but it would be very tight and rather unpleasant. I've run recent releases of Slackware on machines with 98 MB of RAM.

I've run AntiX with the Dillo browser in 60MB, but that will not work with many sites. Even if you get one of the specialist distros like Tiny Core, or do an minimal install of a flexible distro like Slackware, you are still going to be up against the memory demands of your browser.

Thank you for your replies.
OK, so more RAM seems in order, I'll buy some more and install it.
Any ideas about dongles?

Excuse me, but DON'T buy more RAM for that computer. First of all, if you're going to use mobile broadband I assume you'll be wanting to use an e-mail program and a web browser. Neither will run well on that computer. Second, the RAM that computer needs is bound to be of a very old type that would be A) hard to get hold of and B) very expensive. Unless you buy it off ebay. And even if you get say 256 MB of RAM into that old computer it's not gonna be enough. Finally, USB mobile broadband dongles use a connection type called USB 2.0. That computer does not have USB 2.0 and the dongle won't work properly without. Perhaps it won't work at all.

Sorry, that laptop is ready for either a museum or recycling. Or someone who's prepared to use only a text console or a very old Linux distribution on it.

Try peppermint linux, Its fast enough with p3 machines and mobile dongle support is also very good