Carrier 58sxc120 won't ignite and I get a fault code blinking light of short long short don't know what it means.

It means that the unit is getting 24v power. (Normal operation). Whenever a fault is detected, this LED will blink a code describing the fault detected. See the Service Label attached to the unit for more information. (The reference to the LED is near the top).

trans is in sport mode on the shifter there is a button push it and it will go off push it again and it will come on again to inform you its in sport mode

Located on the schematic on the inside of the furnace door should be a key for the blink sequence. 2 short blinks then 4 long ones would be a code 24 on that data plate

Pull any error codes.

The engine light lights up when you turn the ignition switch on, then goes off. After four seconds, if it comes on again and stays on, there is a present fault code. When it is an historical fault code, it comes on with ignition and goes off then comes on and goes off again. I believe in like 4 second intervals. A historical code will not be removed until a cycle of 50 ignition on/of intervals has passed. In other words, the engine light will continue to light two times when ignition switch is turned on, after 50 on/off cycles have passed the historical codes will no longer affect the engine light when starting.
If you will hold the odometer button on the side of the console down, and turn the ignition on and off, three times I think, waiting for the fuel pump to stop before turning the ignition switch to the off position, and one second until you turn it on again, the third time holding the odometer button down until the engine light begins to blink it will begin to blink in a fast sequence showing the fault codes will follow.
First indication of fault code display is rapidly blinking engine light. After that count the number of times the engine light lights up. There will be a brief pause between digits. If there are multiple codes stored, the rapid blinking will separate each. Once the fault codes begin to repeat, you have gone through all stored codes.
Tips: Have a pencil and paper ready.
Maybe ask a friend to help out. Sometimes a second pair of eyes can be good.
Go through a couple of cycles, so that you are sure you haven't missed any codes.
One example is if it blinks 3 times, pause, the blinks 2 times, that means 32.
Code 32: Rear Fuel Injector

Try turning ignition switch thre times, without start engine ( ON / Off / ON / Off / ON ) and count the blinks light two short means a 2, space and one short flash measn 1, so code 21.

Keep us updated.

The D4 light is coming on to tell you that there is one or more fault codes set in your transmission control module. The only way to retrieve codes on the 1995 models is to read "Flash Codes" output by the D4 light. (See instructions below)

RETRIEVING FLASH CODES USING THE D4 LIGHT
If fault codes are present, the D4 light will "blink" when the ignition is turned to the RUN position and will remain on at all times when the engine is running.
To retrieve the flash codes, turn the ignition switch off.
Install a jumper wire between the service check connector terminals.
The service check connector is a gray, 2-pin connector located on the PCM/TCM cover under the passenger side of the instrument panel. (See picture below)

CAUTION: DO NOT use the 3-pin located next to the service check connector.

Installing the jumper will place the PCM/TCM in diagnostic test mode.
Turn the ignition to the RUN position. Codes will be output by blinking the D4 light.
Note the number of blinks from the D4 light. A short blink indicates a single digit flash code. A long blink equals 10 short blinks. For instance one short blink indicates code 1. One long blink and four short blinks indicates code 14. If there is more than one fault code, they will be output one at a time from the lowest numbered code to the highest numbered code. It is recommended that you read the code or codes several times to make sure that you are reading it correctly.

Once you have retrieved the fault code(s) re-post your question and include the information for what codes you have and someone can then help you locate the cause of the problem.

Blinking temp light means bad lamp fan. Needs replacement

First of all when you flip the switch, it goes thru a startup sequence. THEN it turns on the Igniter (notice the red glow). Then the gas turns on.

Now at this point check the idiot light and it should be giving you a code of 34. That 34 (3 shorts 4 longs) says that there was a problem igniting the furnace. After it cycles thru at least 4 times and fails to ignite all the blowers, then is when you get a code 14 (1 short 3 longs)

NOTICE what's happening with ALL the burner Tubes each time it attempts to ignite. If only one or two are running....then this is your problem.
To fix all you do is take out the burner Tubes, look for debris, blow them out (blow from the front where all the jets are), and replace them in sequence from left to right (the tabs overlap).

if you remove the door you see it blinking through there is usually a led diagnostic code list. before removing panel count the long and the short blinks and write the amounts down as you may resett the code by removing the door.
Thanks,
Brian

There is a flame proving device located at the end of the burners looks like a bare wire just hanging there. Take some steel wool and gently rub the carbon off the surface of the wire. It don't take much 3 or 4 stokes will be good.