Gear shifting problem

check tranny fluid level, if not possible faulty transmission control module if not codes related to tranny or issues with shift solenoids

When did you last replace trans filter and fluid? Dirt may be causing shift valve to stick.

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

If the whine is there than the main bearing is already worn adding fluid will not save it, you will have to swap it or rebuild it. sorry i know you were hoping for something better.

Check tranny fluid level and make sure you put in the correct fluid.HONDA SPECIFIC tranny fluid only.

I think if you get a transmission flush your problem will subsibe

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

sounds like it may be either a converter problem or u got some bad clutches in third in the case you need to go to a tranny shop.

you need to replace clutch pack for that gear can be ordered seperately from parts store or dealer if you want to save money call peach street auto recycling at 1800-365-2341 for a warrantied used one! also might be time for change trans filter and fluid filter could be slightly clogged but I lean towards clutch pack I replace these alot on Hondas

that could be a result of your clutch being worn.....or worn gears. have it checked by a professional