Clearly that's not a realistic usage, but beyond that I'd say 35W is a high estimate even during use. CodingHorror has some numbers for a Dell XPS M1330 [1], a laptop from 2008 with a Core 2 Duo (2 GHz) and 13.3" display.
Idle at max screen brightness is 20W, wifi bandwidth test bumps it up to 24W. Running an instance of prime95 pushes it up to 50W, but most people don't do that. Especially with hardware accelerated video, I don't think people are spending the majority of their computer use with the CPU pegged.
A home laptop probably spends 18+ hours a day off/asleep, and the maybe 6 hours of use aren't going to all be heavy loads.
[1] https://blog.codinghorror.com/revisiting-how-much-power-does...
You can obviously buy newer tech for even better power efficiency, but that gets into a discussion of accounting for capital cost vs recurring.
I just put together a home server, I need to get a power meter and see what it's using.
Theoretically if I pegged it out with the screen on max brightness I'd get about 90 minutes out the battery (which is about what linux estimated running stress-ng) in reality depending on what I'm doing I get 5-6 hours and if it's light surfing on an evening over 7. Currently it's saying 3 hours 58 minutes @33% charge, I'm actually surprised how long it lasts given I didn't expect it to but looking at powertop it spends a good chunk of it's time running at about half it's top clock rate and it rarely bursts.
Though to be fair I didn't buy this laptop for it's battery life (I can swap those out if needed) or weight (not that it's excessive) but because it sat on a local maxima for what I wanted (fast quad core with HT, relatively light, relatively good battery life).
The GF's little Asus regularly goes over 10 hours with her using it for the usual net stuff and it's got a tiny battery, it's a cracking little machine but Intellij would wreck it.
5.5 Watts:
My Dell XPS13 with a bunch of browser/slack/java processes on Linux. (it's below 4W at idle)
40 Watts:
My 6-year old Xeon E3-1230 (v1) with 14TiB usable ZFS and 32GB of ECC RAM.
Also, if you're really going for very low power, I'd suggest an RPi Zero W instead of some Android phone. $10 @ MicroCenter and you can install pretty much anything your heart desires from standard Raspbian repos. I can't even measure it's wattage at the outlet with my power meter.
I think I have an APC Back-UPS 425VA (or 600VA) that takes care of that for a sprinkle of RPis, a firewall, an access point and the ONT outside. I like to keep my connectivity during the very brief power outages (underground power).
I've been meaning to try using an Anker portable battery as an extended-run UPS, but haven't tried it, and I don't know if it'll keep the USB port powered on continuously.
I think you'd be better off looking at some of the DIY electronic battery things - eg WiMos battery shield or adafruit powerboost (https://www.adafruit.com/product/2465) and a LiPo battery, but they will only provide ~1 Amp.
If neither of those things are attainable I should be sticking with just using the library's computers to try and manage to produce some form of profit I can put towards eventually getting into community college.
If I'm not dirt broke, this entire article is sort've pointless from a practical standpoint unless you just really enjoy this sort of cost-saving exercise. But if you don't and you're making enough for a real computer then you may as well just get the real computer.
Internet is going to cost way more than $5/mo.
To keep things cheap, I just use my work laptop and an OVH $3.50 VPS for the other things.
A 35W draw will cost you $5/mo at $0.20/kWh. This will either let you run an oldish laptop continuously, or you can go down the path of newer hardware to optimize your constant draw, and spend that energy budget on in-use amenities (nice monitor or faster processing).
But looking at the bigger picture, why would you want to set a limit on your computing costs so low? Today's dominant business model is to use scaled computational processes to trick people into overpaying for products/services. One of the least prudent things an individual could do is further hinder their ability to exercise their own computational agency!