Low power (cheap to operate) server with lots of RAM?

Unusual requirement sometimes benefit from unusual solutions. Sure you can give 6 figures to Sun, Dell or HP and be done with it, but it is not the only game in town.

For single box solutions, getting up to 128GB is very cheap (32 x 4GB ~ USD 3.000), even with homebrew motherboards that cost less than USD 1.000. (don't mock the makers. If it's good enough for Google ... )

256GB is seriously more expensive (32x8GB ~ USD 18.000), and beyond that ...

Alternatively have you considered Infiniband (10Gbps) interconnected cheap boxes as an alternative?

You could build a 4 node, 16 processor (64 cores), 512GB machine that way and still have change from USD 25.000 .

You would furthermore have the added benefits of gracefull degradation, if your application can run on 3 machines if one of them fails, and possibly get a linear scaling in cost up to 8 nodes (just add 4 more nodes). At that point you are looking at a cool 128 core, 1TB RAM beast for < USD 50.000 .

Before you dismiss the Infiniband proposal as exotic, it isn't for the type of machine you are asking for. e.g. 141 of the top 500 supercomputers are built this way, including 4 out of the top 10 ( http://top500.org/connfam/8 )

I would like to build a file server for backups. The server needs to be available 24/7 in a mixed Windows/Linux network, but service should not exceed 1 hour per day. Thats why power consumption is my main priority.

What do you think is the best hardware to build it? What about software ? do you suggest a Linux distribution ?

In my experience, building a PC/File Server from scratch doesn't come close in terms of power efficiency to most consumer level NAS devices. With that being said, full-blown computers are obviously much more flexible/capable then consumer NASes, however home built anything will always consume more electricity. If you're lucky, you may be able to get consumption to within a few watts to consumer-ish hardware, but the time/effort/money may not be worth it.

I have NAS at home hooked up to a UPS, and just with the simple UPS monitor, it ranges from 45W-55W with just two drives. During off-peak times, it can get into the 30w-40w range. I have seen it as low as 25w but that's not common. That's not too shabby. Granted I have a 4-disk NAS, it's easier to operate, small and very energy efficient. Building is always fun but in the end can cost more, have more problems/maintenance, is physically much larger and consumes more electricity than a consumer-NAS counterpart.

Edit1: The server should take 1 to 4 terabyte drives, I'm not aiming at speed, redundancy is not a must, but will be appreciated if not very costly. My budget is kind of limited.

It's kind of odd that redundancy isn't a must considering it's a file server, but to each his/her own. If cost is the biggest issue and speed/redundancy are supplemental, 2-drive NAS devices should suffice.

Off the top of my head, I'd recommend the Netgear ReadyNAS Duo RND2000. It retails around $300+, but look on online retailers and you'll see they sell it for less. I think there's also a big rebate from Netgear on it as well these days but I'm not too sure. Note, Netgear sells most of their NASes with hard drives so prices seem to be inflated. Make sure to search for diskless versions.

Another NAS I'd recommend is the the QNAP TS-239 Pro. I own a TS-409 Pro but I've been very happy with QNAP as it's pretty rock solid. The software it comes with is fairly easy to use and works reliably. It's running Linux embedded so if you really want to dig into the internals, ssh access is available.

2 Disk NASes are fairly economical. The price range is fairly small from $100 to $300. 4 Disc NASes have a wider range of prices that will probably discourage you. They can range from $500-$900+. But it sounds like money is an issue so I'd go with 2-disk in your situation.

Edit2: If I can get a router or a wireless access point to do this job (using USB ports, and probably a modified firmware), then it would be a great idea. Any suggestion ?

I would stay away from this idea. While it may be the most economical/hacker-ish type solution, to me it smells like more trouble than it's worth. I've used DDWRT and Tomato and they're both fine ROMs for wireless routers/firewalls/vpns but file serving isn't something that I saw as a major priority with both projects. I could be wrong these days as it's been a while since I've used/played around with both, but if your files mean anything to you just get a cheap NAS device, hook it up to your LAN and call it a night.