I have a 2006 Dodge Ram Big Horn Edition, with a 5.7L Hemi!! I hear a rattling/fast ticking noise when the transmission shifts is in 3rd gear, stays present while driving. I also feel a weird vibration when this noise is present(3rd and 4th gears)

transmission shift solenoid, google (2012 dodge ram 1500 5.7 transmission stuck in 4th gear) theirs been a lot of problems,
check out forum below
http://www.ramforumz.com/showthread.php?t=74392
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When did you last replace trans filter and fluid? Dirt may be causing shift valve to stick.

follow the lower radiator hose to the engine,you have to raise vechicle to see thermostat it is under the vechicle,the thermostat is in the housing where hose go to thermostat housing bolted to the engine, you need to remove hose.if you have the HEMI ENGINE follow top radiator hose to thermostat housing behind the AC COMPRESSOR.

I thinc the sensor needs inspecting-you need a repair book or go to chilton online for exact location

Maybe try to spray some lithium grease from a can on all of the pivot points for the lower control arms and the shock mounts and spring mounts, etc., that could be making this noise.

If that doesn't solve the problem, maybe have the truck aligned to see if there is a loose part in the front that may be causing this rattle.

Good luck in repairing this problem.

check to make sure that there is no valve lash going on inside the heads and sometimes a crack in the exhaust manifold will do the same thing depending on how fast you are going

Sounds like lifters are bleeding down. Try doing an oil change with a thicker oil or even go synthetic. I use Lucas oil additive and it seems to work pretty good.

Depended on the mileage and if the truck has been worked hard. It could be a few things, A worn out hydraulic lifter, a worn crank bearing, old engine oil that needs to be changed, or maybe a tired oil pump. Try using a stethoscope to narrow down where the ticking noise is loudest. From there you will have a better idea what the cause is. Take a look at the oil pressure, see if it takes to long in the morning for the oil pressure to start building. Every time you look at something different it will help bring you that much closer to the solution.

either repair or replace the transmission...sounds like the sensor went out

ummm i would say you need to adjust your trans shift cable, check your fluid level, and the problem i had with my dodge was similar to yours... it was my 3rd-4th actuator spring, it had broke and couldnt hold the pressure to keep it in gear