Oh well, here goes:
[b]Transmitter Key[/b]
It all depends on the key design, i.e. what chips have been used, but I would have thought 2.8V would be more than OK. This one (non Toyota), I heavily modified a few years ago to control a car PC remotely. It gives up at about 2.5V to 2.6V, but that is due to the small micro-controller I added (small back thing bottom right) and not the rest of the key.
[img]http://i208.photobucket.com/albums/bb315/shcmpb/remote.jpg[/img]
Yes, try not to touch the battery, wipe it clean with a cloth if you do. Make sure it fits reasonably well/tight in its holder or cradle and/or is reasonably tight against the battery contacts in the key and that those contacts are clean too. I know some manufacturers have had to put a good deal of effort into battery holders in the past, to overcome problems with loose batteries.
Of course, there are a whole load of things that can go wrong with the key. For example, if the mechanics are not well designed, repeated operation can flex/crack the PCB (printed circuit board) itself and/or produce hairline cracks in some of the small components on the PCB. This can be difficult to spot without a microscope, but can lead to intermittent operation.
As an aside, ECUs very often have a "drop test" specification that they have to pass during design validation. Usually about 1 metre onto a concrete slab. It is mainly so that if the ECU gets dropped by a fitter on the car assembly track, it doesn't break. In the past, a few manufacturers also applied this spec to the remote locking key, not thinking that keys go through much more abuse in that respect, (thrown across rooms or from windows for people to catch etc).
If you know anybody with a scanner/receiver, you can do a very basic check that the key is at least transmitting every time you press the button. Usually (although not always) it will need to be tuned to around 433.92 MHz (Europe) 315MHz (US, Australia). Very often, the data rate from the key is low enough to be heard on the receiver. Try both AM and FM.
However, the fact that you are having problems with both keys, suggest the problem is with the vehicle and not the key.
[b]Receiver[/b]
I never went looking for the receiver on the 4.2, but this suggests it is near side rear:
[img]http://i208.photobucket.com/albums/bb315/shcmpb/rlrx.jpg[/img]
The first thing is to get up close to the vehicle in roughly the position of the receiver, and see whether repeated operation works OK. Just bear in mind that on some vehicles, the electric door latches are not designed for rapid repeated operation. If they are operated a lot, they tend to get hot. In the past at least, some manufacturers have implemented a "latch cool off" feature in the body controller software. After too many rapid lock/unlock operations, the latches are deliberately not operated for a while, so they have time to cool down.
If that works consistently, then there is a possibility the receiver has gone a bit deaf. High temperatures can reduce the sensitivity of the receiver (you get an increase of noise in the receiver itself while it is hot). One manufacture found under heavy solar load (lots of sun

), the locking range reduced considerably. The ambient temperature where they had mounted the receiver exceeded its temperature design spec a fair bit.
Yes, you can get interference from various sources, that can reduce the receiver sensitivity or in some cases block it completely. That is several topics in itself (in a former life I've been involved in trying to fix or improve badly designed receivers with respect to this).
Is your garage metallic? Or does it have a large metallic door? A signal bouncing around in such a structure, can, in some instances, be easier for the receiver to hear. (Operating the remote locking at long distance on some empty high speed ferry car decks can sometimes be interesting). Have you installed anything else non-standard electrical in the vehicle?
What happens if you hold the key higher (or even above your head) while pressing the button? Does it improve things? (There's some peoples old favourite of holding the key under your chin too).
Just remember, a large percentage of vehicle electrical problems are simple wiring or connector problems. It could be something as simple as a bad receiver earth, or if it has a separate antenna (usually they don't), a bad connection with that.
Very difficult to fault find these things remotely (if you'll excuse the pun), but just shout if you have more questions. Good Luck!