Dodge Repair: 2003 dodge neon: vibration cause?

Question
Dear Sir:
Greetings! Purchased used 03 Neon SXT, 131,000 miles on it. Nice car but steering wheel vibrates  excessively at idle. Had all engine mounts and tranny mount replaced. ( 1,151,00 dollars ). Had throttle body cleaned out. ($ 182.00 ). Still vibrates!! Mechanics said next step is to disconnect tranny from engine to see which component it is. Does not change vibration when shifting into neutral, reverse, etc. ( auto trans. )
 Any idea what it could be?? Thank you for your time and help!!
Jim R.

Answer
Hi Jim,
It would seem that the engine/trans mission unit as a whole is vibrating, correct? The engine has a vibration damper mounted on the crankshaft at the front of the engine and that may be defective, so consider that possibility.
It may also be that one of the cylinders has a 'miss'. I would begin by having a fault code readout done on the engine unit using a plug-in code reader that attaches to a socket under the dash by the steering wheel. The fault codes are 4-digit numbers preceded by a P. A shop will do that for about $40 and sometimes nationwide auto parts stores (e.g. Autozone) will do it for free. Ask for the number(s) and what they mean. Then ask a follow-up question and we'll go from there.
Please read the PS (below) and respond to it.
Thanks for doing that.
Roland