Hi Nathan,
Welcome to the DJU Forums

. If you are looking the advice then you've come to the right place.
Firstly, we've all been 15 (Some further back than others

) and not being able to drive, and have no income etc. However, technology has come a long way since I was your age and the solution may not be too far away.
First of all, any expensive equipment is out, so spending $1000 or $2000 at your local DJ-Store isn't worth even considering and besides to start off with, I doubt that you would need a mobile DJ level of gear in any case.
You obviously have access to a computer to post on this forum

, so why not put it to some use musically?. If you check out the DJ and PC section of this forum you will find several types of software mentioned - all of them have free downloads and trials lasting for upto 30 days. Even if you choose to buy the software, after 30 days it will still be a lot cheaper than buying Decks and CD Players.
It sounds like you may be more interested in going into Scratching and Mixing, rather than the "mobile" aspect of D.J'ing at family type occasions. If this is the case, then read the section on Scratching and Mixing and you may also like to post a question to Alex (Fenix842) Shaun (DJSBD) or Mobile DJ Crookes. All 3 of these members are in the same age group as you, and all have a keen interest in mixing!.
IF you choose to go into D.J'ing further, then you will eventually need to invest in a pair of turntables or a Dual Cd Player and a Mixer, perhaps even 2nd hand just to start you off, but I would follow the computer option first and download the free trial versions of the software available. This is the only real free way of D.J'ing.
Another idea, would be to see if there are any local youth or community groups running D.J type workshops in your state?, perhaps ask at your School if they know any courses or youth organisations that teach Mixing or D.J'ing?. Another option would be to contact a local D.J and ask if you can help out at his "gigs", although given that your only 15, you would need to discuss this idea with your parents first.
If you need any more advice then just post!, and we'll try and help you. We all had to start somewhere and learn the business.