We only have fourth gear in our manual transmission

If you have the five speed manual, almost certainly the fifth gear is an overdrive gear. Overdrive means that the gear ratio is less than 1:1, and in most 5 speeds, the fourth gear is 1:1, the fifth gear being less, such as 0.85:1 for instance. So yes, you probably have overdrive, it's just not called that in a standard transmission.

Which transmission does yours have 4T65-E or 4T80-E ?

4T80-E
No Fourth Gear

Checks

Causes

1-2 Shift Solenoid Valve
?€¢
Inoperative
?€¢
Debris
?€¢
Pinched wires

3-4 Shift Valve Bore Plug

Misassembled

4th Band

Burned, slipping, missing

4th Servo Cover

Cracked

4th Servo Pin

Broken, seized

4th Servo Piston

Damaged

4th Servo Seals

Rolled, cut or damaged
4T65-E
Slipping or No Fourth Gear
Slipping or No Fourth Gear Checks
Cause

DEFINITION: A large engine RPM increase is noted in fourth gear, Drive range, with little or no vehicle forward speed increase. First, second, and third gear operation are normal. Shifts into fourth gear are soft or do not occur. Fourth gear ratio is 0.705:1.

Automatic Transmission Fluid Level
Low fluid level

Transmission Main Line Pressure
Low transmission main line pressure

Oil Filter Assembly
• The oil filter assembly (100) is missing, plugged, or damaged.
• The oil filter seal assembly (101) is missing or is damaged.

Control Valve Body Assembly
• The 3-4 shift valve (362) or the 4-3 manual downshift valve (360) is stuck or binding.
• Debris is found in the passages of the control valve body (301) or of the control valve body spacer plate and gasket assembly (396)

Case Cover Assembly
Distortion or damage occurs at the manual valve (404) or at the case cover (401), causing PRN oil leak.

Driven Sprocket Support Assembly
A plugged third clutch oil passage in the driven sprocket support assembly (609)

Fourth Clutch Assembly
• The clutch plates (500-502) are worn, damaged, or misassembled.
• A missing or not seated fourth clutch spring retaining ring (601)
• A damaged spring assembly (602) or piston (603)
• Worn or damaged fourth clutch piston seals (604, 605)

Third Clutch Sprag Assembly
• The sprag (720) was misassembled or backwards on the inner race (661).
• A damaged third clutch sprag assembly (653, 661, 719-721)

The gearbox synchromesh gear is worn out . The box needs to be reconditioned or exchanged

Sticking valves. When is the last time you had the transmission serviced? Since it will shift when cold, I would suspect a valve body issue.

The manual transmission uses a mainshaft that is locked in 4th and gives the 1:1 ratio. The rest of the gears come off the input shaft of transmission to a counter gear cluster then back up to output shaft. Either the input shaft gear or the gear on the counter shaft is stripped. That would cause the only fourth gear drive.

Is it a manual normally if that is the case your looking at large problems clutch or transmission it self to cause this.

check your transmission fluid level it may be low.if not get a transmission flush as fluid can be dirty

sounds like the syncro for fourth gear is warn out you need to take it apart to repair it

This is what your codes mean:

Trouble Code-P0734 (A/T Additional Gear Ratio Error In Fourth Gear)


Trouble Code Conditions:
Vehicle driven to a speed of 4-37 mph at more than 500 rpm, gear selector in 4th Gear in Drive, and the PCM detected too much difference in the engine speed and output shaft speed.
Possible Causes:

• Customer may complain of intermittent 4th gear operation
  
• O/D and 2/4 pressures less than 75 psi
  
• O/D or 2/4 clutch volume indexes out of specification
  
• O/D accumulator seals are damaged
  
• Transmission enters "limp in" mode running in 4th gear
  

Trouble Code-P0735 (A/T Gear Ratio Error Fourth Prime)

Trouble Code Conditions:
Vehicle driven any forward Gear, and the TCM detected the ratio of the Input speed to the Output Speed did not match the current Gear Ratio (this test can take up to 5 minutes).
Possible Causes:

• Related Gear Ratio trouble codes may be stored (note that some of these Gear Ratio trouble codes may be intermittent)
  
• Transmission has internal problems or damage present
  

You have a transmission problem.Hope this helps, James Booth

if its jumping out of fourth back into nuetral then you have 2 options,both involve taking out the gearbox.
1/replace the baulk ring on fourth gear or
2/ get a recon box(poss the easiest,as all rings/bearings will have been replaced).