I am looking for a low power, low end pc able to run 24/7 without overheating and a way to support it in case of power failure. Power failures can be up to 72 hours.

The pc dosen't need a monitor or keyboard. A modem must also be protected in case of power failure.

When i say low end, i don't mean crap. The cpu needs to be x86 and have at least 1k cpu in this chart: http://www.cpubenchmark.net/index.php

What's the best way to do this?

EDIT: more info.

I need to run a home server. The server will perform light tasks mainly. A x86 cpu sadly is the only route for my use. I want to be able to run the server and the router/modem in case of power failure.

Now, regarding how long the power will fail:

1) 1 hours is OK for most situations. (say 90%)

2) 3 hours is OK (say 98%)

3) 6 hours is more thank OK. (say 99.5%)

4) On extreme cases the power might fail days. I believe this is very unlikely to happen. More is great but, really, how ofter power will fail more than 3 hours? I believe once every year at best. Well, that's too rare to care about.

Given the above, I am looking for a cost effective way to archive 1-3 hour power or 6 hour if possible.

Solutions:

You guys give me great ideas.

1) Power generator: no good as power will fail for 10 seconds before returning. Also I read online, "clean" power generators cost 1.5k+, so it's out of budged. Non clean generator might damage electronics, right?

2) Solar power: i don't know for sure about this. Sounds like a great idea, too good to be true, honestly. For only 200$ i get 100+w? What are the drawbacks here?

3) UPS: This seems to be the best. The only problem is the cost.

Cost

< 200$ = great 400$ = budged limit