Sounds like for a low cost job you are wasting money in some respects. Unless you have very very soft subgrade and need to spread the loading some on subgrade, base course is not needed. Four inches thickness concrete is a BARE minimum thickness. I'd shoot for 5 inches thickness and the best quality of concrete. If you have average soil, just give it some compaction if you can, as by driving back and forth with a vehicle. The main thing you need is strong concrete, not really needing re-bars. I assume you know about cement content and water-cement ratio needed for strong concrete, as well as what proper curing. As to joints, if you keep slab units no more than about 8 feet long (or square), no special joint filler is needed. Wet the subgrade just before placing concrete so that there is no variation in water content top to bottom. Otherwise bottom will be stronger and shrink less when finally things dry out. Otherwise a slight curl will occur. The only excuse I would use to say use some base course is for ease of getting a reasonably uniform thickness due to ease of grading it. For background it is well known that highway rigid pavements benefit only slightly by using base course under for carrying the loads. A driveway hardly even approaches the same requirements. Save your labor and money on what is below the slab, but spend your efforts on the concrete. Re-reading your post there is a quesiton. Are you mixing your own concrete? If so what sort of mixes, etc.?

I will be using ready mixed concrete, 4000psi pea gravel, 5% air. I was able to remove a few pieces of concrete from the damaged area this morning, and probe the subgrade. There's about 2 or three inches of mud, as I expected but below that it was actually pretty firm, so I don't think I'll have to worry about any soil removal, other than the mud on the surface. As for the cost of the project goes, concrete around 500$, and approximately 200 for miscellaneous. I would prefer a concrete contractor to do the work but have talked a couple of contractors just to see what they would charge, each one were in the 1800-2000$ range for demo and replacement. Since I don't mind performing hard labor on occasion, I'm electing to diy it.
Any recommendations on performing the demo?
Another question I have, what are your thoughts on creating what would essentially be a Construction joint to reduce the size of the demo. To elaborate, I'm dealing with two adjacent sections of concrete separated by an expansion joint, with two sections above and below.(6 total sections make up the driveway, 2 at the top, 2 in the middle, 2 at the bottom). All sections are approximately the same size. With the failed area contained in the upper half of the middle sections. Would removing only half of the section be a solution worth looking into. Generally speaking, I would install smooth dowels in the lower half of the section, placing them on 12" centers (I'm guessing on the spacing). I'm not sure if it would be aesthetically pleasing-I know it wouldn't initially, but I was thinking it would be less noticeable as the fresh concrete aged. It would not be a cost saving measure, more of a reduction in back breaking labor during the demo.

For a construction joint you need a concrete saw. Rental for that seems excessive to me, but I have fitted a 12" chop saw with a concrete blade and arranged it to do slab cutting once to save the rental cost. Needs water for the job also. Dowels seem to me to be asking for trouble. Once they start to rust and possibly expand and break out concrete you won't like it. You can call for 4,000 psi concrete, but play with too much water then what is the strength. This table may help. I usually call for the mix as number of bags per yard, not strength.
http://www.mid.org/isc/iscd-3-misc.pdf

In my experience the problems with small jobs like this is not expansion but shrinkage.

The question I might ask is why did one area fail? Was it a souped up job at the end of the load left over from another site?

JimGriffin...to follow on the excellent advice from oldest guy....

Your thickness is too low. That could be one reason for the initial failure. I would go to a thickness of 6".

Next, you are using a high shrinkage mix. A 4000 psi pea gravel mix requires a lot of cement and correspondingly, has a lot of shrinkage. Use a mix design with a larger aggregate. You can get 4000 psi mixes with a 1" nominal coarse aggregate size. This will have lower shrinkage than a pea gravel mix.

OG is right...you will have more shrinkage than expansion. Don't worry about expansion. Cut control joints every 10 to 12 feet each way and make sure the divided areas are almost square....with a maximum aspect ratio of 1.2 to 1. (12 feet in one direction, 10 feet in the other). Cut the joints the same day as the concrete placement. If you wait until the next day, very fine shrinkage cracks will have likely already developed, so you'll get cracks in locations other than the control joints. When you cut the control joints, cut them to a depth of 25 percent of the concrete thickness. This will give you 75 percent for aggregate interlock and some load transfer across the joint. I also would not use dowels, since those require a bit more expertise to install properly than you will likely have on hand.

For the demo, go ahead and rent a concrete saw. You can rent a wet saw for a week for about $150. You can use that to pre-saw the slabs and then break them up with a sledge hammer into pieces you can handle. The added benefit is that you'll have a wet saw available when you place the new concrete so you can sawcut the control joints quickly as they should be done. As soon as the concrete has set enough that the saw does not cause the coarse aggregate to ravel, you can cut your joints.

Yes, you can replace the section that is damaged. I would replace the whole section, not half of it. The concrete appearance will even out after a year or so.

"... Dowels seem to me to be asking for trouble. Once they start to rust..." You could get coated dowels and if you cut to length coated rebar for dowels, there is an epoxy system you can use on the bare metal ends.