If the 400 were in good shape it might be worth $35 to a collector, but... as noted, it's a difficult machine to meaningfully use. Besides the keyboard, which is really basically only good for interacting with games, the other problem with the 400 is that it *probably* doesn't have enough RAM. They shipped with as little as 8k, which isn't good for doing much more than running cartridge games. (I think stock configurations topped out at 32k... I had one of those I paid $10 at a garage sale for around, erm, 1992? Judging from the box it came with, covered with *NEW, now with...!* stickers it was probably one of the last ones made.)
If you wanted to go full-blown retro-challenge on it you *could* dedicate yourself to maxing it out. If you dig around you can probably still find the instructions for upgrading the RAM to 48k (I believe it can be done via either piggybacking 16k chips or swapping a set of 64k chips in and cutting traces.). Once upgraded a 400 is essentially interchangeable with an 800, and from that point, well... at minimum you'll still want a BASIC cartridge. That should be one of the easiest cartridges to find, but
AtariMax sells flash cartridges that could probably do in a pinch . (You might even be able to find an editor/assembler ROM image if you really wanted to go nuts. Atari BASIC is known for being slow and it doesn't really include much support for taking advantage of the graphics and sound capabilities.) But if you're going so far as buying the multicart you'd probably also want an SIO2PC cable so you could run APE and emulate disk drives and other peripherals... or if you really want to keep it old school, get yourself a couple drives and an 850 interface box. And by the time you spent the money to get all those items separately you'll probably be over the cost of buying a single bundle of Atari 8-bit stuff all together. (And said bundle would probably include a better programming machine like an 800xl.)
In short, if you were already an Atari collector and had peripherals and software to use with it $35 for a working 400 is probably reasonable. But if you're starting completely from scratch... no. (If it had the BASIC cartridge it might be a maybe.)