It appears to be a TFX PSU but I'm not certain. You need to look closer.
When I see something like THIS which is only 350W (420W wasn't in stock) for $88USD
https://pcpartpicker.com/product/sFjG3C/seasonic-power-supply-ss350tgmretail
My suggestion is to get a cheap, normal ATX case then move everything over and just use a normal ATX PSU..
I'm NOT sure if this is all compatible, but perhaps something like this:
https://pcpartpicker.com/product/T3rG3C/cooler-master-case-nse200kkn1
and
https://pcpartpicker.com/product/FQ648d/corsair-power-supply-cp9020101na
I'm aware the above has a rebate on, so you probably need to use the rebate to benefit but maybe you could buy the PSU and put the rebate towards the case?
UPDATE:
http://static.nix.ru/autocatalog/hp/hp_computers/202282_2235_draft.jpg
If you zoom in, I think that's what your PC looks like inside...
Several PROBLEMS I see here:
a) no graphics card slot?
b) proprietary CPU blower cooler only works with similar case
c) power delivery?... I suspect it's 24-pin and hidden beneath the metal support but I can't be certain
d) what motherboard form factor is that? (it may be micro-ATX but I'm not 100% certain)
Hmm...
OKAY, I think it does have a graphics card slot (that card in the middle), and the BLOWER should exhaust out the rear of any case if you want (or be replaced with different cooler).
I do think you may be able to transplant this into any microATX or ATX case (with an ATX PSU) but you'll have to think about it... also, an ATX style case allows you to put in a DVD player/burner if you want.