I have a 1994 Lincoln Mark Vlll.when it shifts into 4th gear,it starts to **** when I press on the gas lightly

Great JOB!

possible that clutch has failed, to test do following
switch off engine and put gear into 4th, with brakes on try to start
engine while in gear. if the engine starts switch it off straight away

this confirms your clutch has failed, if engine stalls your clutch is good.but could mean that the clutch activator is not working. either way
recomment you see a qualified dealer or machanic about this issue.

I hope this was helpful

first thing to check is transmission oil level and quality. If that is fine than your looking at either a valve body problem (valve body is what controls the selection of gears) or possibly a problem with the bands on the planetary gear set, they can be tightened in certain models. However i dont think it is the bands.
Does the overdrive only engage 4th gear? or does it feel like the gear ratios are different between overdrive and normal before the problem happened? some overdrive buttons engage final gear and some do as much as change gear ratios like in a cvt (contantly variable transmission) and some just change the timing in the gear changes to provide more rpm/power.
My best guess is that the valve controlling the overdrive in the valve body has failed and therefor you dont get a response from the transmission (i.e no gear shifting when overdrive is selected)

Check make sure the throttle cable is not binding inside..I would watch the throttle cable and with the vehicle off mash the throttle several times ,make sure its returning back to position..Also move the throttle under the hood and remove the duct work and make sure the butterfly valve inside the throttle body is not loose from the linkage outside

For the 1993 thru 1998 Lincoln Mark VIII 4.6L DOHC V8:

Firing Order:
1 - 3 - 7 - 2 - 6 - 5 - 4 - 8

Cylinders:
..........(back)...........
|...4...|..........|...8...|
|...3...|..........|...7...|
|...2...|..........|...6...|
|...1...|..........|...5...|
..........(front)

Coil Connections:
............................
|.1..6.|.........|.2..8.|
|.5..3.|.........|.7..4.|

Let me knowif this helped, or if you have additional information or questions. Feel Free to contact me at FixYa.com!

I found this one the www.hondacarforum.com
http://www.hondacarforum.com/honda-technical/28562-i-have-1989-honda-integra-can-any-one-tell-me-what-s4-gear-stick.html

You have a couple of choices on this Honda transmission... D and S modes. Consider the D as the normal Drive mode and the S for Sport mode. The difference between the two is that in "D", the transmission will shift through the gears all the way to 4th gear and at lower rpm shift points. In "S", the transmission will shift at higher rpm levels and will go no higher than 3rd gear and light S3 on the dash. Once the vehicle is in 3rd gear (S3) you can then press the S4 button and the transmission will go into 4th gear (when conditions dictate). I believe there is even an S4 indicator on the dash signifying the trans is in 4th gear

The last line looks like it is the key here though.

If the car thinks its in 4th gear when you are trying to start it, obviously it wouldn't start...you could probably hunt around and see if there is a sensor on the transmission stick that runs the "D" vs "S" mode

Save your self the hassle and expence of troubleshooting and replacement parts, install a suspension retrofit kit which changes the rear bags to coil springs and the front to struts. A car this old you might as well start over for less than $500.00......

change trans fluid / filter

Possible shift solenoid problem . Do you have any idea how the electronic shift control works ? Your best bet , take it to a qualified repair shop. Have it checked for DTC'S - diagnostic trouble codes .

I found this one the www.hondacarforum.com
http://www.hondacarforum.com/honda-technical/28562-i-have-1989-honda-integra-can-any-one-tell-me-what-s4-gear-stick.html

You have a couple of choices on this Honda transmission... D and S modes. Consider the D as the normal Drive mode and the S for Sport mode. The difference between the two is that in "D", the transmission will shift through the gears all the way to 4th gear and at lower rpm shift points. In "S", the transmission will shift at higher rpm levels and will go no higher than 3rd gear and light S3 on the dash. Once the vehicle is in 3rd gear (S3) you can then press the S4 button and the transmission will go into 4th gear (when conditions dictate). I believe there is even an S4 indicator on the dash signifying the trans is in 4th gear

The last line looks like it is the key here though.

If the car thinks its in 4th gear when you are trying to start it, obviously it wouldn't start...you could probably hunt around and see if there is a sensor on the transmission stick that runs the "D" vs "S" mode