Clutch will allow me to turn the car on but I am unable the shift gears.

Hi,

First, congrats on the most detailed problem description I have ever seen! Seriously, it does assist us.

All this is completely consistent with your clutch not releasing properly, meaning that the gearbox is still turning when the pedal is depressed. The syncros in the gearbox will then keep you out of gear, that is what they should do. You can indeed shift into higher gears however when driving as the gearbox revs more nearly match to what is needed. The jerking forward when you hit the starter is due to the poor old starter motor having to move the whole car instead of just the engine, because the clutch has not released !

Now as to why, it is likely that the clutch release fork has broken, inside the housing. I had this once with a Mazda, and symptoms were exactly as you describe. The gearbox has to be removed if this is the problem, and you should also then take the chance to renew the clutch, pressure and driven plate both, unless quite new.

Also a possible cause is a complete loss of clutch fluid if a hydraulic clutch, or a broken cable if that type of clutch. Loss of fluid in a hydraulic clutch can be easily checked in the fluid reservoir, and can occur if a hose splits
..

Eric, how are you confirming whether or not the car goes into gear if you shift gears without the engine running? One way would be to put it in 1st and see if you can push the car. If you can't, it is in gear.

Another option is to roll the car slightly forward or backward (engine off) while trying to put the car in gear. Once it is in gear, then the car shouldn't move any further. However, if it goes into gear, DO NOT start the car without taking it back out of gear.

The clutch is much more likely to be the problem than the transmission.

If the clutch fluid ever ran dry, then the clutch hydraulics will need to be bled of air. Otherwise, the problem could be the clutch master cylinder, slave cylinder or throwout bearing. Since you didn't report the clutch slipping (e.g. engine revving without accelerating when in gear) it is likely not the clutch disks themselves.

transmission synchronizers most common cause of transmisson noise in certain gears, and not others, might want to check the gear oil level. Transmission rebuild required. To read about them and what they actually do, then here is a good read:
When you shift gears in your standard shift car, you move a rod that moves a fork that engages the gear. Depending which gear you're shifting to, a different fork does the job. The fork moves the collar to the desired gear, and dog teeth on the collar mesh up with holes on the gear in order to engage it. You engage reverse gear through a separate, small idler gear. The reverse gear always turns in the opposite direction of the other (forward) gears.
In years past, double-clutching was common in order to disengage a gear, allow the collar and next gear to reach the same speed, and then to engage the new gear. To double-clutch shift, you pushed the clutch pedal to free the engine from the transmission. Then the collar moved into neutral. You released the clutch and revved the engine to get it to the right rpm value for the next gear so the collar and the next gear spun at the same rate to allow the dog teeth to engage the gear. When the engine hit the right speed, you depressed the clutch again in order to lock the collar into place on the next gear.
Modern cars use synchronizers in order to avoid the need for double-clutching. A synchronizer, or "synchro," lets the collar and gear synchronize their speeds while they're already in contact but before the dog teeth engage. Each manufacturer's synchro is slightly different than the others, but the basic idea is the same. For instance, a cone on one gear will fit into a cone-shaped depression on the collar. The gear and collar synchronize their speeds thanks to the friction between the cone and collar. Then the outer part of the collar moves out of the way so that the gear can be engaged by the dog teeth.

A shift solenoid controls oil flow to the clutch packs in an automatic transmission. It uses DC power to turn them on The clutch packs control which gear you want The torque converter is basically a slippable clutch when you accelerate it engages and drives the gearbox

adjust the clutch padel

The transmission in a Volkswagen vehicle shifts gears only when there is enough hydraulic pressure. This is made possible in part by the clutch cable, because it connects the clutch pedal to the clutch master cylinder. The clutch master cylinder in turn transforms the foot pressure that is carried through the clutch cable into hydraulic pressure. If the clutch cable breaks, the clutch master cylinder will be unable to generate enough hydraulic pressure for shifting gears.

sounds like your clutch is not disengaging. when you press on the clutch pedal you should feel the resistance of the clutch pressure plate. There is a pilot bearing in the flywheel when it goes bad it continues to turn the transmission mainshaft not allowing your gears to line up for a shift, but you have noticed a bad noise if this were the cause. Or your clutch hydraulics have gone out. check your fluid level. if low you may have sucked some air into your system. you will have to bleed the lines as you would for car brakes. The other possibilities are bad clutch master cylinder or slave cylinder,

You have one of these two things going on....Either the clutch master cylinder is internally bypassing or the clutch itself has gone bad. If you can pump the clutch and sometimes be able to shift, the master is bad. If the clutch pedal feels normal, then I'd suspect the actual clutch disc is worn out.
Your clutch has little to do with shifting with the engine off as nothing is turning and engaging the gears is not a problem. Have an experienced tech take a look at it if in doubt ...should take all of five minutes to determine what's wrong.

There is a clutch fork and it's bolted to the transmission bell housing. It's what pushes on the clutch bearing, disengaging the transmission from the engine, which allows you to safely change gears. If it's broken, you will surely have to replace that clutch fork in order for you to do any gear shifting in the future.

You may possibly have a defective clutch slave or master cylinder. Get this fixed immediately as it will cause problems with the gear box.