Hi
@Denv12I am replying as I like computers but can't say I'm an expert at all. I am happy to provide you with some ideas as I know fixing a broken computer/searching for a new one can be a pain!
A computer case isn't worth much, the expensive parts are on the inside which are probably toasted as you mentioned lightening strikes.
For $350 you may not be able to find a new desktop pc but there are some new laptops online around this price point. There are also retailers that sell 'refurbished' pcs which are basically second hand ones that have been tested,cleaned etc. for sale. If your old monitor works, you may be able to hook it up to a laptop - have two screens.
It's also worth considering whether you want to buy from a shop - easier to have someone to talk to if you need advice or a problem - or buy online.
There are lots of second hand pc's on gumtree etc. but a bit riskier buying second hand as it's unlikely they'd accept returns.
Apart from gumtree, trading post etc. you could do a google search for "laptop under $400" and "pc under $400" and see what you can find.
Happy PC hunting!