Aha, my favourite! I've also got a thinclient that I got from work - no optical, small hard drive, the usual. DSL and Puppy both install fine. Vector .... Vector of any flavour is a bit trickier. But hey, challenges are what keep life interesting, no?
First of all, I'm assuming you want to do a full install, not merely run from the USB stick, correct? If I'm not, that's fine - I'm also interested in learning how to run Vector from USB stick as opposed to HDD install. But if you do wish to install, the first thing I'm going to recommend is to grab the iso-install script from
here. For the record, I use a 2GB stick for this sort of thing, so I'll again be assuming that you will too.
Now, place the install script, and the .iso of Vector on the thumb stick. Boot your thinclient using DSL (I found Puppy to be a little quirky doing this, though Puppy does a far better job of preparing the partitions with GPartEd - swap between them as necessary), drop to run level 2 (Ctrl-Alt-F2, login as root, "init 2" without quotes) and then navigate to your mounted thumb drive. From there, run the iso-install script.
It
should work. It really should. The reality is, it probably won't the first time - It'll either hang on extracting the image or creating an appropriate "proc" directory - I think this is something to do with DSL, I honestly don't know. Either way, should that happen (and the folks who know better than i do about this will now cringe) comment out the offending command. If it's the image extraction, you'll have to fiddle - I can't remember the commands exactly.