I don't know what type of budget your working with, but unless it's incredibly and food-stamp type low, I really think that you may not be looking hard enough. Before attempting any half bakes ideas (All the advise above is great, I'm not referring to that council), I'd suggest 3 things. 1: obviously, try the used sport shops. Often times you will get low quality bags, but the good thing about a bag is it's not there to look pretty. Even strapped with duct tape, it still does it's job. 2: and this is kind of out there, but i've done it. Go to a few boxing gyms, and see what they have available. I'm talkin, beat up, run-down type places. Throw in some cash, and you might get lucky and walk away with a cast-off. Chances are slim, I know ...usually that sort of stuff goes to those who train there, but again, couldn't hurt. The good thing about boxing coaches, is many of them understand hard times, and are willing to help serious trainers. or 3 ...Garage sales man! look around! Heavy bags are alot like Total Gyms, or Stair Masters, in that alot of pseudo-macho types buy them jus to show'em off, maybe hit it a few times, but usually just get rid of'em later ...You might get really lucky and walk away with one heck of a bag for 20 bucks.
Otherwise, yeah ....Shadowboxing, and mitt's are great ideas. I'd also recommend shadowboxing underwater. Sounds weird, but give it a shot. One heck of an exorcise, at least.
"Life is a myriad of probabilities. Living is a plethora of possibility."