Car problems, of all sorts, HELP please

By the way i just joined the forum, very nice by the way.
Any who, back to the matter at hand, i bought my 95 Neon off my parents about a month ago, they previously left it in the driveway for 8 months not running. Before, my mom used it to drive back and forth to work and stopped because of engine problems. They shop she took it to told her that it was a chip in the motor that was bad. So I ordered a new chip, im not sure the specifics of which one it is, but it mounts over the left front tire (http://forums.neons.org/viewtopic.php?f=1&t=334037&p=2710641#) well. I put it in, drove bout a mile down the road and nothing changed, so i know its not that specific chip.

But these are the problems so far:
1) HESITATION. The only way i can describe whats happening is hesitation. Ill start the car, back out of my driveway and the car stalls. Ill put it in park, then start the car again, then continue backing out. (Its an automatic) Once in drive and im actually moving, ill step on the accelerator, and the car will start accelerating but then stop, my foots still on the gas, and it wont accelerate, then in like a second or two it will pick up again. Sometimes it will do it my whole trip (round 11 miles to college), and others it will from the time i start it, til half way home be working fine, then the hesitation will kick in again.

2)DIEING. This problem didn't present itself when i first started driving the car, but has now surfaced. Every time i come to a red light my car will start shaking, and i can hear the engine idling really low, and then the engine cuts out. To prevent this i have to, when approaching a red light or a stop sign, i have to shift into neutral and lightly accelerate to keep the engine from dieing.

3)SPEEDOMETER. When i used to drive the car on the highway up around 75 mph, i noticed one night while looking down the needle on my speedometer started goin insane. Up to 75, then down to 40, up to 60, down to 20, up to 45. To be honest it looked like it was "dancing." I have a video of it and can post it on youtube if anyone wants to see it. Also sometimes when driving on Route 50, at about 55 mph, the speedometer dies, the needle goes straight to zero, and wont go back to my speed unless i restart the car.

4)REAR BACK UP (http://forums.neons.org/viewtopic.php?f=1&t=334037&p=2710641#) LIGHTS. The rear back up lights wont turn on. While getting it inspected the shop told me about the back up lights, they checked the fuse and it was fine, and offered to replace them so i figured y not. After they replaced them they still wont turn on, and the "mechanic" said he had no idea why. Big help.

5)TAPPING SOUND. Sometimes when the Neon is hesitating real bad i hear occasional "tapping" noises under the floor just above and behind my seat. Like something is actually hitting metal, and i know im not hitting something, cause it happens from a dead stop sometimes.

I've heard different "solutions" from everyone, my friends, my grandpa, shop mechanics, and no one can come up with an actual answer. I've already taken it to one shop who left the car in the lot for a month, and afterward told me they had no idea and charged me money for it. If anyone could offer an answer or some advice I would greatly appreciate it. And hell if it actually fixes some of these problems I'll even send some money your way for your troubles.

I also keyed the ignition and got the following:

flash (pause) flash flash = 12
flash flash (pause) flash flash flash flash= 24
flash flash (pause) flash flash flash flash= 24
flash flash flash flash flash (pause) flash flash flash flash flash = 55

Any suggestions?
Any and all help is GREATLY appreciated. http://forums.neons.org/images/smilies/good.gif

Anyone know if a bad or malfunctioning TPS (throttle position sensor) could cause any of this?

Yes the hesitation and the stalling problem.

Well first of all, there is no "chip" for the engine. So what the hell did you replace?

The code 24 is for a bad TPS (throttle position sensor). You can try pulling it, and giving a good cleaning. Also inspect the wiring for any exposed/bare/frayed wires. If that's all good, it probably needs to be replaced.

Code 12 is for a battery disconnect within the last 50 key-on cycles and code 55 is end of codes.

The speedometer is a common problem on the neon....the joints on the back of the circuit board need to be re-soldered...
http://www.automotiveforums.com/vbulletin/showthread.php?t=480855&highlight=cluster

You may also need a new backup lamp switch.

Besides possibly getting a new back-up lamp switch, you might want to take the tail-lamp housings off and see if there is water in them & corroded lamp sockets. Because the gap between the rear fenders and the lid for the trunk channels water down onto the top of the tail-lamp housings, a lot of rain water goes past there. Some of it can easily run into the lamp assembly, and build up to a depth of a few inches. Then the overflow runs into the trunk and makes it wet. I took off the tail lamp assemblies and drilled a hole in the bottom, so water could run out. Then after re-installing the tail lamps I put RTV sealant across the top of the lamp, so rain water would not drop into the plastic assemblies.