depends. If the whole lot came as a system, its the retailer that sold you the computer's problem.
If your budget PSU exploded, destroying other PC components that weren't from the same retailer, technically you could bemand the retailer that supplied you with the budget PSU pay to get the other companents fixed.
You would however need to prove (within reason) the PSU was not fit for purpose and that you were not using it beyond its spec.