You could absolutely install 2kw of solar for probably around 2-4k and then at worst it turns your daytime usage into 0$. I also would be surprised if this was pulling 1kw in reality, I would want to see an actual measurement of what it is realistically pulling at the wall.
It could have zero marginal cost, right? In particular, if you over-provisioned your solar installation already anyway, most of the time it should be producing more energy than you need.
No need for battery and battery is by far you largest cost. This could 100% just fallback to grid power, it's not backup power it's reducing usage.
Not sure about where you are but where I am a 2kW plus li-ion batteries is about 2months of the average salary here, not for tech, average salary, to put it into perspective converted to USD that is 1550 usd. Panels is maybe 20% of that cost, you can add 4kW of panels for 450 USD where I am.
So for less than the price of that PC I would be able to do 2kW of solar with li-ion batteries and overspecing panels by double. None of that cheaping out on components, can absolutely get lower than that if cheaping out. Installation will be maybe another 500-600 USD here, likely to be much higher depending on region. Also to put it into perspective we pay about 0.3 USD cents per kWh for electricity and this would pay for itself in between a year and two in savings.
By the time it needs to be replaced which is from 5-7 years on the stuff I just got pricing on it would have 100% offset the cost of running.
Again I am lucky and we effectively get 80-100% output year round even with cloud cover, you might be pretty far north and that doesn't apply.
TLDR: it depends but if you are in the right region and this setup generates even some income for you the cost to go solar is negative, it would actually not make financial sense to not do it, concidering a 2K USD box was in your budget.
I believe it was an 850w PSU on the spec sheet?