Air conditioner goes off and on, only hot air and when the air conditioner goes off the dash lights get dim and act strange.

Make sure the battery has a full charge and all connections good. Then check your charging system. Right now I'm thinking, check your charging system.
Do you have a voltmeter on your dash, what does it do when you step on the brake? It may drop a little, but, it should recover.

Lot of time car cut out you speedometer cut out or dont start key on no check engine on the dash

You could replace the sending unit to cross it off the list of possible problems.
You could check resistance cold and then with the engine at normal temp too. The gauge on the dash could be faulty too.

There are 3 things to think what can be the problem.
1. there is a day/night sensor on the dash.{not working properly}
2. there is a variable dimmer for the cluster illumination. loose connector or terminals.
3. The display itself.{can be defect} loose connection at the display or terminals.
lot of work.

Hope it helps.

You need to check for a loose ground again. The dash seems to have a loose ground. Your heat and ac are controlled by motors that get input from your switch. You might try following that harness and see if there is a loose ground. Other than that I don't have a clue. You might also check near the firewall and make sure the ground strap there was bolted to the engine.

Better start with the controller if it is malfunctioning. If it is the all elctronic one, may not be sending signal to turn on compressor.

Your issues can not be answered easily or definitively, as the LS is very complex and all electronic.
I would need the stored codes,that set the check light (MIL Light)
You can cycle the right dash display to ACFilter and Reset,with the top row of buttons,in center of dash. There is no sensor on the Cabin Filter. All the dash displays, are just reminders,you can set any way you want, % wise.

Possible issues--Fuses
-- Coolant control valve
--DATC module

You will need a really good Technician,not a general mechanic, to diagnose your problem
You need to put a professional scanner on it, to start any diagnostic work

Hello, It sounds like your hot/cold blend door actuator is either hanging up at times or it's loosing it's calibration range because it's starting to go bad. The ticking noise is most likely the actuator trying to close off the hot air port but is unable to stay closed allowing hot air to mix with the cold. If it's just a weak blend door actuator, it will act up more when the air is on full because it has more resistance due to air flow. If possible try to see if the times it acts up decreases when you start the A/C with low fan speed.

On most cars when you push a button or slide a lever to change your choice of location where you want the air to blow out louvers move inside the dash to redirect the air to your chosen location. When you switch from heat to AC other louvers move. These louvers are often powered by vacuum lines running from the engine. If one of these louvers is stuck or if you have a vacuum leak in one of the lines it may be causing your problem.

responded already.