you should invest in some CDRWs

i found some that are like 10 years old and i have been using them for livecd testing because i was tired of wasting cds.
have you tried SliTaz?
it claims that it can work in as little as 16mb ram, but it runs fine with 256.
except for me, apparently nobody else in the world, i have some issues with the browser closing by itself, like in the latest puppy linux.
if you just want to use the internet, and dont care much for the other functionality,
http://browserlinux.com/ may work for you. it works great for me, unless i try to add too many extra programs. but it comes with firefox 3.5.5. and flash 10, it is based off puppylinux 4.3.1 but does away with all the applications, and fixes the crashing of the browser that is the plague of puppy linux.
but just one CDRW and you could try them all. no more trashing cds. the cdrw i use for browser linux even has its data layer flaking off around the edges, but the data only takes up a small portion of the center.
i know what you mean though. it is a very long search to find a distro that even runs on 256mb ram nowadays.
if flash player/etc are not important to you, or you know how to install packages for slackware(i dont) you should totally check out "Mitrax"
i have had zero problems with it, besides not knowing how to get packages. it looks like the guy was going for a win95 lookalike.
http://www.mitrax.net/ it comes with opera web browser and mplayer, and i dont know how to install anything like flash, java, apps, anything, but it is the most stable distro i have tried. SliTaz i like very much, if i could get it stabilized.
oh, looks like i put some topics that don't belong in this post, like.. i cant install knoppix to hd, and i donotlike DSL. anyways, those are some recommendations, and
http://tinycorelinux.com/ as well, but of all 3, mitrax is the most stable for me.
if your laptop touchpad has a scroll wheel section, some distros won't use it properly, especially if they use xvesa or something like that.
i am in the same boat you're in, downloading loads of livecds, testing them and they dont all live up to their claims.
some claim to be 'lightweight' and then ask me for 1gb of RAM.
i also like Antix, but it did ask me for a little over 2gb of hard drive to install on.
it should run on your system.
Antix may be my favorite, since SliTaz closes the browser on me. i'm not sure which ones autorecognized the wifi, if your old computer uses wifi.
so, i cant help you with your debian live lxde problems, i have my own problems with it. i can't even find where to set up my IP on it. . but i posted to recommend to you the best live cds i have tested lately., and cd-rw's, and if you can boot from USB, you can save all those CDs by using Unetbootin and a flash drive, and the iso files.
Antix, Mitrax, SliTaz, Tinycore.
Antix and SliTaz are the most feature-packed, and good looking, and tinycore has a package manager too. i liked its looks but i forget what problem it gave me. Mitrax looks kinda like windows 95, but never gave me an error message or froze. they are ALL better than DSL, unless you can't install packages, then DSL might beat Mitrax because DSL has the Aim, IRC, all that, even though they are text based. and a package manager.
i was testing them all with a 1.30ghz celeron with less thann 256 mb ram usable, but cpu speed isnt as important with these distros as RAM is. and i never tried them with over 2gb of storage because no hard drive, just 2g flash drive.