My RR3 Jackson Guitar has corrupt sound.

Here is a link to the Jackson serial number info

I would say, that it probably needs a new 9V battery. It had some time to gain some juice after the gig. If a fresh one doesn't help, then the problem could've been the equipment or power outlet distribution at the gig site.

You might try a washburn 7 for great jazz sound

I would suspect the tremelo hardware is not returning to rest at the same point. Look for rubbing points and maybe lightly lube those... very sparingly.

It sounds like somehow the pre-gain is very high while the volume or post-gain is very low. Try turning the volume high on the effects unit and the gain low, and don't have the amp volume too low either.

Distortion is not produced in the guitar. Distortion is generated in the amp by circuitry that increses the gain until the waveforms "flat top". This creates higher harmonics and a buzzy sound. If you are getting a very low output from your guitar it is possible that you don't have enough output to get the distortion in the amp to work. Other settings in the guitar add harmonics by mixing more than one pickup. This is not ditortion but adding these harmonics changes the sound immensly.
LOOK AT THIS SITE AND FIND A SCHEMATIC THAT MATCHES THE RESOURCES OF YOUR GUITAR... You might be able to figure where the wire goes... It may be a ground.

http://www.guitarelectronics.com/c=D65u46R1H9tko6CKpPLsjBhiJ/category/wiring_resources_guitar_wiring_diagrams/

Instructions on how to re-string your guitar can be found here:
http://www.justinguitar.com/en/TB-003-ChangeStringsElectric.php
If you mean something different by rewire please let me know.

i dont' see where this model has active pickups (guessing this is what you mean by pre-ampped).
The issue can be in a few places.

1) the strings could be too far from the pickups and the instrument needs to be tuned.
2) the pickups are bad
3) your jack is bad
4) the cable is bad
5) your equilizers are not corrected
6) your volume control is turned down or damaged
7) your amp is damaged

this is a small list of the basic possibilities.

String gauge is a personal preference. I'll ask you this: what is your playing style? I see your picture and its a Jackson DK2M. One thing to remember is that the Floyd Rose usually needs adjusted with a different string gauge. With a Floyd, I recommend replacing one string at a time unless you are cleaning the neck with steel wool. If you are taking all the strings off at once and changing them all at once and not one after another, put a towel under the back end of the Floyd Rose so it does not tilt back and mar the finish. Jackson usually installs 9's on their guitars, but this is too light in my opinion.

The pickups...there is a screw on each end of the pickup to adjust the pickups up and down. Raiseing them will get you more output but more noise and feedback. Lowering them will get you a more mellow sound. I keep mine no less than 3/16 to 1/8" from the strings.

Bridge adjustment...Floyd Rose trems are tricky little animals. They have small allen screws to raise the saddles up and down. Raise the bridge just enough to keep the strings from buzzing excessively and as long as they don't make a buzzing sound thru you amp, its nothing to worry about.

Send me a message if you have any more questions. With a Floyd Rose, it would not hurt to go consult your favorite guitar shop or a friend with a Floyd equipt guitar to see them work on them.

I can say with a fair amount of certanty that this is the control knob on your guitar, these are fairly cheap and if you have any mechanical ability you can replace it yourself, there will be some soldering involved so if you can't do that I would take it to your local music store and most have some sort of repair department, this shouldn't be a big bill to get fixed.