You'll need to find out what chipset the ethernet is and find the appropriate Linux kernle driver. Hopefully it's in the SliTaz-compiled kernel, else you'll need to compile it and/or request it's inclusion in the next update.

WRT the DVD burner, it should 'just work' if it is recognised as a CDROM drive. BurnBox should do something useful but I can't vouch for it as I've never used it. Other burning software may be available.

HIH.

okay thank you so far seawolf
I typed in lspci and this what it said for ethernet controller: 'nvidia corporation MCP77 Ethernet'.
Now how do I figure out what driver is the right one? and how do I activate a driver that is listed when I type: modprobe -l | grep drivers/net
(is it the "modprobe -v 'modulname'" command?)

I think the easiest way to figure out which driver is the right one for me, is to figure out which driver is used by slitaz-live, because that one works.
How do I do that?

Yep, that's exactly right.

If it works on the Live CD, open a terminal and type:
lsmod
to tell you which modules are in use. Hopefully you'll be able to recognise one, or it's logically named!

I normally just google for them! The site:
http://cateee.net/lkddb/web-lkddb/FORCEDETH.html
tells of the *forcedeth* module, can you load that with modprobe?

I take it that you've a nVidia nForce motherboard? Perhaps nVidia have such kernel modules on their site?

Maybe someone with a similar mobo can help more than me!

so, my motherboard is called K10N78FullHD-hSLI by ASRock.
and lsmod (in slitaz-live-firefox with working internet connection) responds:
k8temp 3820 0
hwmon 2028 1 k8temp
snd_hda_codec_realtek 179412 1
snd_hda_intel 22020 1
snd_hda_codec 49928 2 snd_hda_codec_realtek,snd_hda_intel
snd_hwdep 5988 1 snd_hda_codec
snd_pcm 51780 2 snd_hda_intel,snd_hda_codec
snd_timer 16344 1 snd_pcm
snd 43584 8 snd_hda_codec_realtek,snd_hda_intel,snd_hda_codec,snd_hwdep,snd_pcm,snd_timer
soundcore 5180 1 snd
snd_page_alloc 7256 2 snd_hda_intel,snd_pcm

If any of those modules is the right one, I don't know which one it is :)
oh and it's not forcedeth, I tried that.

okay, solved the problem...
I compared the output of lsmod of the slitaz-live version with the output of the installed version and guess what... they were the same
so I started playing around with the networkconfiguration and changed eth0 to eth1 and everything works fine now!
thank you anyways seawolf!
greetz
-Nik