Why would my Daewoo Matiz 800cc not gear down to 4th and 2nd gear?

Question edited for clarity, 'Matiz' not 'Martiz'.

https://www.google.com/search?q=2004+Daewoo+Matiz+cylinder+head+torque

Just change the search query to the other parts and press enter.

'year make model (the part) torque'

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You are looking for the torque settings for big end bearings and main bearings on a daewoo matiz?
Main bearings torques on a Daewoo Matiz 800cc (1999)
Stage 1: 25-30 Nm
Stage 2: 55-60 Nm
Big End Bearings…

The fact it only has a possible misfire in the first 3 gears,
tells you your under a high vacuum load getting up to speed
& applying more gas pedal command as well, until you let up
in top gear

Timing is engine load related, so your theory is not valid there either

I would do a cylinder leak down test to check the mechanical condition
of the motor,valves & such,then use an evap smoke machine to test
intake,exhaust & evap system for vacuum leaks

What about EGR System Even electronic ones use vacuum,thus
my vacuum load theory.

Get rid of all ignition misfire issues

No Vacuum Leaks anywhere on car

New upstream O2 Sensors or scope yours for
switching times

Check timing belt for issues

I guess you checked fuel pressure

Check alternator for bad diodes

Need a scan tool to look at fuel trim & all data
on a road test

Basically you missed something

will be clutch cable or clutch hydraulic system fault depending on what car it is could be clutch assembly sticking clutch plate on splines will not be gearbox fault if you can select gears ok with engine turned off

it could be your oil preshure is not up to par or some times if your idle goes to loe it can set off your lo speshure light but i just cant be shur so give it a look but do watch it please

It may be the synchro of the first gear.  It may have been worn out.  To check, you may try to put it in 2nd gear before putting it into first to be sure.

Tighten the cylinder head bolts to 85--90 NSm (63--66lb-ft).

2001 daewoo matiz 800cc

This is the best info I have.

Just as important as the torque values is the tightening sequence. Since modern engine heads are soft alloys this is key. The bolts are tighten down maybe half the final value on the first pass and then tighten down fully on the final pass.
The Sequence is; 7 1 3 5 8 4 2 6 bolts 5&6 are the flywheel side of the engine Torque values Stage 1. 40-45Nm first pass Stage 2. 85-90Nm. second pass

Since you have the head removed look for carbon build up on the pistons.
You may want to get a car service manual from the library or on the internet.

If the clutch feels firm with no play u may have worn syncronizer's in the trans, take it to trans shop and have them road test it, they will not charge in most cases.

if it wont drive how do you kno its engaging if it is in gear and you arent pushing in the clutch it should move forward if it doesnt move then you will have to replace the clutch