Although cheap, that's not actually the cheapest way to mine.

The cheapest way to mine would be to head over to eBay and buy something like a Block Erupter/Ice Fury/Antminer U-series or any other obsolete stick miner for $5 and mine with that. It wouldn't be profitable of course and you might not be able to reach the pool's minimum payout threshold (you could always opt to solo mine instead however) but at least you would still get the full mining experience, if that's what you're after.

Anyway OP, if you're still interested in mining with your computer then you could try mining altcoins and converting these to bitcoins using an altcoin exchange like Cryptsy. There are many altcoins out there which can still be mined using CPUs or GPUs. The only ones which have ASICs built for them are SHA-256 based coins like Bitcoin and Peercoin, and scrypt-based coins like Litecoin and Dogecoin.

Here is a list of CPU-mineable coins:

http://www.cpucoinlist.com/

(Note: It hasn't been updated in a while though so some coins might have transitioned over to GPU mining since the list was written. To the best of my knowledge, no ASICs have been developed for any other algorithm besides SHA-256 or scrypt however.)