If you were going to buy a decent sounding/performing pair of 'computer speakers'...

You want something self-powered that sounds pretty good at less than $100? What about SIZE? Because the M-Audio AV 42s are currently on sale (Amazon) and are OK for anything in this price range for desktop applications. But may be too big for you?

Take a look:

http://www.amazon.com/M-Audio-AV42-Professional-Monitor-Speakers/dp/B00X741TB0/ref=sr_1_2/185-2218359-8906642?ie=UTF8&qid=1448650543&sr=8-2&keywords=m+audio+av-40

You can also try to find the previous model on sale if its still available, the AV-40. Not really a true studio monitor but as good or better than most computer speakers, but a tad bigger.

Audioengine A2's are amazing. I think on sale for around $200 right now. Not sure if a used pair would fall down in your budget or not.

Ima go witt two 5/4" x6"x 24" pine boards with a hole cut into them and a raw driver super glued to the backside. THEN!, use a large NH stone to stabilize the base. Maine stones will not work here.

Dump finds put you out about $0.78!

Zinga!

I have these in my home office and like them: http://www.amazon.com/Definitive-Technology-Incline-Audiophile-Desktop/dp/B00G5CKH6O/ref=sr_1_1?s=fiona-hardware&ie=UTF8&qid=1448722702&sr=8-1&keywords=Definitive+technology+incline

I guess that's out of your budget, but if you're looking for powered and decent sounding it's gonna be tough me thinks...

I use the Creative Gigaworks T20 at work and find them to be very good and well below $100 at $59 a pair:

http://www.amazon.com/Creative-GigaWorks-Multimedia-BasXPort-Technology/dp/B001RNOHDU/ref=sr_1_1?ie=UTF8&qid=1448722971&sr=8-1&keywords=creative+gigaworks

I also have a pair of the larger T40 speakers at home and find the bass can be over pronounced on those but they have bass and treble controls to control for placement issues. Either pair is good for desktop nearfield use or use in a small room with a computer as a source, and they aren't overly large. They sound larger than they are and produce an excellent stereo image up close with a cloth dome tweeter. They can also be used as a pair of speakers for a TV set in a smaller room. Another plus is the front panel auxiliary input, so it's easy to have the speakers permanently hooked to a computer while also accepting a temporary connection from a phone or tablet.

Another speaker in the price range is the Bose Companion 2, but those lack built in tone controls and are expensive for what they are.

I'll give a third endorsement for the Klipsch Pro Media 2.0's .
If you get bored with the stock satellite speakers, you can remove the little volume control unti from them and run a different pair.
I added a couple of those old Mirage Omni egg shaped speakers to my rig and it sounded awesome !
In fact, I sold that system to my neighbor, who uses it to power his electric keyboard. (he's a church organist) and I can feel the floors rumble when he's playing the pipe organ settings over there. (heh heh)

I run a pair of M-Audio Studiophile DX4s. They're probably the most accurate 2 channel computer speakers I've had in the price range. I've had the Promedia 2.1 system and personally I find it really harsh. They do get insanely loud and will rock out like no other pre-assembled computer speaker system however.

I also have used a pair of vintage Minimus 7 Realistic speakers on random amps and love them - not a simple setup however like you're asking.