A bit late to this but if you look at the labels on the bottom you see a number of things.
1). The Xbox has at some point clearly been opened from the fact the torx screw heads are visible and have wear and tear.
2). The label shows that it was manufactured in October 2001 confirmed by the product ID code too (week 41/01).
3). Factory location is more difficult to be certain of as there is contradictory information about the codes in this respect. But 03 apparently means it is from the Hungarian factory and therefore a Xbox v1.0. Again the date supports this.
My experience is only with PAL consoles and none include that additional label in what looks Japanese. That suggests it could be a J-NTSC model made for sale in the Far East. For practical purposes* it makes little difference although the primary language setting (easily changed) may not be English.
4). If it is a v1.0 when you open it up there should be a fan on the GPU heatsink and the USB controller on a separate daughter PCB.
5). The connection out of the back of the Xbox could be a fan switch but from the position on the right (as looking at it) more likely to be for a chip. That, of course, suggests the Xbox is modded.
6). The DVD dongle (specific Xbox DVD Remote Control required - not supplied as standard) on the front (controller port 3) looks broken OR could be it has been modded to be a USB port. You can still get Xbox port > USB (F) adapter cables very cheaply but a mod like that is a nice little extra even if crudely done.
7). The whole amateur paint job, quality of the work and general look of the thing is poor and bearing in mind its age I'd be surprised if it was functional. It also does not show any controller or leads so $20 is more likely to be $35 unless those are included.
8). The weak component of the original Xbox is actually the DVD drive. If that is completely broken the Xbox may not work at all. If it is just mechanically broken the Xbox will function but it will limit how it can be used.
The only practical fix is to buy a replacement DVD drive and that will cost you as much as another used Xbox and as such renders the original Xbox purchase pointless.
If the Xbox itself and the chip is working that would still make it reasonable value IMHO. Personally I'd take a punt on it if it could be tested beforehand. If it turns on, if you get a video output of some sort, if the DVD tray ejects OK and, particularly, if the chip is present and working then it just might be worth it.
* The power supply (figure 8 socket) label clearly shows it is a 100V model so make sure it is compliant with your location's mains voltage before use.