My bare minimum (my every day laptop) is my Lenovo Thinkpad T400 from 2008 (Core2Duo T9400, 4GB RAM, hdd & 900p display). Bought it for 100 a year ago. Didn't feel doubling the price of it to add an ssd was worth it.
It's good enough to run KDE Plasma 5 without locking up at all. It struggles when using some heavier IDEs like Android Studio but perfect for text editor development and the likes.
I do admit to having a much more powerful desktop though.
My BAE screams for coars, so minimum of 12 for me.
#gentoolife
i needed a pfsense box.
so an old sempron 145 , 4GB ram, a small ssd , several network cards (dual WAN) and a old case/psu were pressed into service. most of which i had lying around anyways.
i tried to unlock the sempron into a athlon IIxe , but it had several strange issues. i have returned it to its sempron roots to test this.
Why don't you just... get a new case?
Really I just need a high end CPU for rendering work and a reasonable GPU for the times I play games (only play at 1080p) and I have more than enough of both.
If it wasnt for that I would rock a core2duo or something all day with no problem.
My rig serves my needs just fine. It's a simple fx6300, 8GB ram, 2GB 270x, and a couple hard drives (no ssd because idgaf about speed. 30 second boot time is enough for me to get all situated anyway).
I have but 1 absolute need: Can it play Carball?
I also like it to run Warframe, minecraft, gtav (idgaf about the settings... came from console so anything is better than that), and a few other low demand games. I play games that I find fun, not ones to test my system. I enjoy playing games not running benchmarks.
That's just my Linux PC, so nothing really fancy needed. I just got any case that just works.
On another hand though, I am planning to get rid off that case I have owned for just over a month. The way you mount the top fan is odd; you need the rails to even mount one 120mm fan on the top. Otherwise it's a no-go. On Ebay, there is a user who has these rails I need but going by the cost and also the shipping cost too, I find it too uncalled for to get them, where I could get a Corsair 800D for just $135NZD.
All I need is a decent quad-core, 8GBs of memory, 1080p display and Linux but naturally my current setup out weights those requirement by quite a large margin but anything lower than those requirements would make it difficult for me to get stuff done.
Does it really work if you need to zip tie the radiator? 
Zip ties are a perfectly valid mounting solution for a lot of things.
They are basically brand agnostic universal mounting hardware.
Bare minimum, as is pure need without any extras? A laptop with a cpu that can playback 1080p youtube video I'd say would be enough for most of my workloads, as that is probably the most demanding task. 2GB RAM. A usb port and a sata to usb adaptor. A linux distro and 40GB of storage.
Edit: oh and some wifi capability and an audio jack 
There we go.
Then you can even extrapolate a whole bunch of other tasks from that.
You mean a tablet? Because a tablet is basically exactly what you described there...
Yeah though I'd like there to be support for a free distribution of Linux. Probably should have added that. Also it would make my life a lot easier if I could have a hardware keyboard, that's why i said a laptop.
keyborrdz r bttr
That is what I would consider a mobile device for ... mobile device things like you described. And @psycho_666 is right in pointing out that it gets fuzzy around that performance level. But of course form factor and architecture is also a thing. 
My minimum carry around computer matches your description. (It isa little higher spec but it serves that purpose) Still, I need the photo stuff, just not all the time.
I was going to type almost the exact same thing except i dont "need" a ssd but since they cost the same as a mechanical drive it's kinda silly if you don't use one for at least the OS
Need is always such a loose term when it comes to computers.
Well I would put into the "need" category because once you get used to systems with SSDs everything else looks so slugghish also for a portable device like a notebook is a gosend because if it takes a hit or get's dropped you're not going to lose all of your data.
P.S. i forgot to say that it's a bit more power efficient than a traditional HDD
