2004 buick century,hesitates going into reverse and drive then shifts in hard.

SOURCE: transmission error code P1750

Might be really simple - but EXPENSIVE! I had a similar fault - apparently the first planet set breaks up. Cure - a new box. Price - crippling!

Don't be tempted to skimp on the box. Get a rebuild from a reputable supplier. A s/h box will set you back around £5-600 in UK where a rebuilt (guaranteed) will be more like £1800. The thing with the cheap box is it costs about the same to fit but you don't know how good it is till it's too late! Then you're still shopping for another but you're £600 lighter!

Also, you could be buying other faults. If the speed sensor has had a problem - the box will change badly (snatching) and that will be another £250 where the expensive box will have ahad one fitted!

SOURCE: lincoln ls shifts hard into reverse

You will have to have the solenoid body replaced in the tranny and have the PCM reprogrammed.

SOURCE: gear shift won't move out of park sometimes

look for transmission shift interlock solenoid fuse.or a bad brake switch will cause transmission not to come out of park.

SOURCE: automatic transmission wont catch into any gear

You sould have been moore frequent on your transmission fluid changes, and you shouldn't have taken it to Jiffy Lube either. Your best bet is to drain and fill the trans fluid run it shift gears. Drain and fill again. Do this 3 times. Yeah the transmission fluid is expensive. on the last drain and fill you want to get a bottle of LUBE GUARD from NAPA or who ever sells it. put the whole 10oz bottle in. Shift Rev, 1, 2, 3, D. Neutral Rev D. If that don't work then you have bad seals.

SOURCE: buick 2001 century check has the code p1404. is

Hello Momma.
This code has set because a fault was detected in the exhaust gas recirculation system (EGR).
If your car is running normally, no chugging or rough running, it isn't a serious issue. But you should have it looked at to determine why it set.
Often it's because the pin inside the EGR valve is sticking or carboned.
If this valve sticks it can allow exhaust gas into the intake when it should not be and cause your engine to stumble at idle or low speeds.
It will not damage anything over a short period of time.

Thank you for using FixYa.
Best of the season to you.

KL