Go to Synaptic>Settings>Repositories. There will be a couple alternatives in the drop down that shows a repo name. Click on that and pick a different repo.

If not sure, try "other". Among other things it will offer to ping all the mirrors and pick the fastest one from your box.

This is not always the best choice as it may be a little mirror with no traffic at the time you try that option. It will work though and be good to know that one is available.

This will alter your /etc/apt/sources.list for you. Hit the reload button and you should be all set.

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Thanks Caravel. Finding another mirror did solve it. I replaced the kernel.org repository with one from York University, and it now works.

Personally I would advise against this method for several reasons - most notably that you will never understand the sources.list file syntax (it's very simple indeed once you get used to it) and thus will be effectively crippled if xorg breaks and you're e.g. faced with a virtual terminal wanting to change repos to pull in a package from another branch...

There was a thread at the debian forums some months ago where someone reinstalled the whole OS just to generate a new sources.list file...

There is a howto here for editing and understanding sources.list: http://www.debianuserforums.org/viewtopic.php?f=9&t=388

(It's not a complete guide, but it gives a noob a decent run down of the minimum they need to know.)

When you see "could not resolve" it means that your networking is borked or the mirror is down. For future reference, in such cases you only need to replace the mirror, thats this part: "http://mirrors.kernel.org" with one of these:

http://www.debian.org/mirror/list