97 t-bird vibration at all shift points

Fist thing is ..any dash warning indicators..light a Service Engine Soon" light?

Emissions controls and sensors are monitored by your vehicles on board computers... for their proper operation...which allows the vehicle to run as clean and efficient as possible.

You need to check for logged OBDII diagnostic fault codes.

Some Auto Parts stores offer this service free of charge. Check your local shops for free code reading. You may find some codes, which will provide a starting point.

Could be as simple as a O2 sensor.

More info here:

Oxygen Sensor

Major transmission problem. That's what the flashing Check Engine light means.

If the Check Engine light is on all the time, it means there is a "fault code" stored in the computer. Take it to an auto parts store (like Auto Zone) and ask them to read the codes to see what it says. They should do it for free. If they won't, go to another auto parts store.

P0420 = catalyst efficiency below threshold (bank 1)

I think it is a coincidence that the check engine light came on with this code at the same time as you installed the new alarm.

the power train control module or computer checks the output of the oxygen sensors (pre-catalyst and post-catalyst) and compares them. When the post-catalyst sensor output starts to resemble the pre-catalyst sensor output with little difference, the computer sets the catalyst efficiency code. Check the output of the oxygen sensors. A worn out or lazy oxygen sensor might be at fault. If the sensors check okay, then the catalytic converter may need to be replaced. This is unusual for a 2005 unless the engine has been having misfires. Raw unburned fuel will quickly destroy a catalytic converter.

could be a lot of things. try going to advance auto parts and see if they will hook a diagnostic computer to it. They will usually do it for free.
At least you'll have an idea where to start.
Hope this helps.

I have the same problem with my 04 Sequoia, I wish someone would answer this question.

the check engine light usually flashes to indicate a misfire. if you go to advance auto they will scan the car and read the codes for free, you can add them to your question and they may give you a best guess, to me it sounds like an oxygen sensor or a mass airflow sensor which will effect your air fuel mixture causing the car to run badly.

Run into an autozone, or Pep Boys, or other big autoparts store & ask for a free trouble/fault code scan. Once it's scanned & codes recorded, if solution not obvious, get back to us with codes & we will help you.

I looked up the codes you posted.
P0420 is showing a bad oxygen sensor on bank #1, the one down by the catalytic converter.
P0773 is an electrical problem with the shift solenoid E.
A bad oxygen sensor would cause lower fuel milage.

first you need to find out the code auto zone or advance auto should give you a code reading , i try to help but without the trouble code im lost

I agree with emissionwiz, there are tons of reasons. My best guess would be an oxygen sensor. My opinion is that these are most likely to go bad. They only last around 100,000 miles on a car. On a 97 though, they should be able to pin point which sensor is giving you the code. Take it back to them, or try a different store such as Advance Auto and see if they can give you a better code. You should have a P00000 code from them with the OBDII diagnostic system that your vehicle has!

- Matthew