Feeble, cheap, but internet connectable computer w.o. screen and keyboard

what hardware/computers are there out there that might fill this bill?:

the kind of situation i want to set up is to have a few sensors, say webcams, feeding into a computer, which runs a piece of software i’ve written to process data from the sensors, then over a normal broadband (uk) connection, send the results of the processing to a webserver. the part i’m asking about is the computer. i want it to be asbolutely as cheap as possible. it does not have to be fast or lots of memory or hd space. it needs to have the caperbility to have webcams connected to it and the ability to connect and send over the internet, and to run my code. that’s it. something like the mac mini, which is a computer without keyboard and screen but it’s not cheap or crap enough. so what computers are there like the mac mini, but way cheaper and more feeble?

going to an extreme, probably too much of an extreme, there’s things called microcontrollers (e.g. http://en.wikipedia.org/wiki/PIC_microcontroller) but even if there were a way to physically connect those to the internet, the code to do so would be needed (which is what OS’s supply) so they’re almost certainly too small/feeble. but is there anything down towards the end of the spectrum where microcontrollers are, which can be connected to the internet does anyone know? failing that, back up to more normal computers, are there any smaller more feeble cheaper mac mini like computers that anyone knows of?

thanks.

oops, forgot about this thread, sorry. thanks v. much for the info, will look into those.

thanks.

Via EPIA motherboards?
http://www.via.com.tw/en/products/embedded/boards/index.jsp

some mini-cases
http://www.mini-itx.com/store/?c=3

Step 1: visit newegg, zipzoomfly or your favorite online pc retailer.
Step 2: Pick out a combo package that fits your budget: it will have a mainboard, cpu, and ram - the mainboard will have onboard video, sound and lan.
Step 3: select a case, with PSU
Step 4: select a HDD that fits your needs
Step 5: optional: select an optical drive
Step 6: pay < $300 (US)
Step 7: wait, assemble, install, test