I have a 1996 Ls400 and I have 2 issues I can't quite pinpoin the problem.

First issue is when the car is off I hear a sound coming from the engine bay..(seems to be from this little black box under the drivers side light.) The sound is very distinctive and hard to describe, sounds a bit like an alarm system beep but more muffled.

Second issue is, when I cold start my car and put it in drive it gives quite a big kick forward, i've never owned a car that pushed so hard when put in drive,. This doesn't seem normal to me since this is ment to be an ultra smooth car.. could this be a tranny problem since imo the shifting could be smoother as well

 

maybe the tranny mount needs replaced

 

The sound, is it one beep or is it constant beeping?
Your car jumping when you put it in gear, is this before it is warmed up? When cold it idles 600RPMs, or more, higher then when warm. That would cause the car to lunge forward harder when put in gear. Also, the tranny mount could be worn out but that would make you feel the jump on the shifter.

 

It beeps once every like.. 10,15 seconds.. it's really weird.. it stops after a few minutes.
Regarding the tranny I don't feel anything wrong int he shifter itself.. the only weird thing on the shift is that I hear a clicking sound very loudly when I press on the brake when the car is in Park position.

 

thats the neutral safety switch. when cold my 97 idles almost 1200 RPMs and it lunges forward pretty significantly if i put it in gear. let your car warm up before you put it in gear.

 

Yea I have the same sound as well just after I turn off my car and is coming from the front end around the radiator i kinda don't know how a mechanic could diagnose it because it goes away. I also have my 96 LS kick forward if i don't give it enough warm up. When the engines warm it give no kick at all. Why does take so long for this model to warm up even in hot weather I mean i take a good 3 to 5 minutes in warm weather and like almost 10 minutes in cold weather...

 

i had same hard kick when i shift from park do drive when i bought mine 2000 but for it was low transmission fluid
after i ad some fluid no more kick even in cold weather and on cold trans