Chain not catching and noise

If it has the 2.2L engine, and its has more than 60K miles on it, you may have had a timing chain jump. The tensioner for the chains breaks and allows the chain to jump time. They only last about 60-80K miles before this happens, and when it does, it usually bends valves in the head since it is an interference engine. GM knows about this and has done nothing to correct it. You need to do a compression test to confirm the problem. If it shows low compression on one or more cylinders, plan on a replacement or rebuilt head and a new timing chain set. Then either get rid of the car or plan to replace the chain tensioner every 50K miles to prevent it from happening again.

I speak from personal experience here, having had it happen twice on my daughter's 1997 Cavalier.

It sounds a lot like 3rd gear and shift fork need replacing, it seems a very common problem on the r6, jumping to a higher rpm would mean it is jumping out of 3rd and back to 2nd.
There is a slight possibility the spring and ball, that locate the shift drum,isnt holding it in gear.

Super glue or duct tape

If this is occuring at speeds of less than about 5 to 10 mph or during slow speed parking lot types of manuvers then the problem may be due to an ABS sensor at one of the front wheels. The sensor develops a very small build up of corrosion beneath it which pushes it away from the sensor tone ring just enough for the signal to degrade and for the ABS to think the wheel is locked up which, in turn, activates the ABS system which, in turn again, gives you the pedal jump and can extend the braking distance. When I find this type of problem I usually replace both of the front wheel sensors and clean up the mounting surface to fix this problem. Sometimes the problem can be seen using a scan tool that shows the actual readings the sensors are producing but many scan tools aren't quick enough to catch that data.

Check timing chain. Shoot a timing light at the marks on the crank, and see if they are jumping around or staying in one place. If theyre jumping a lot, the chain has jumped. If there is no light flashing at all, it may be broken, or coil, or etc. Check those first.

It is possible that the first gear shift fork in the transmission is bent causing the 'dog-clutch' between two gears to just barely mesh. With engine off, push the shift into first and clutch lever released. Rock the bike back and forth to see if the gearing seems to be jumping in and out. There may be a problem with the shift lever shaft mechanism not allowing a complete shift into first gear. Hope this helps!

Assuming the engine will turn over, the ratcheting assembly on the kick starter may be worn. Remove the kick start lever and then the side cover, (place a pan under the bike to catch any oil). The kick starter is basically just a gear and a spring; the gear will in some manner engage the flywheel, (sometimes indirectly). Make sure there is nothing obvious wrong such as broken teeth or debris lodged in the mechanism.

The other possibility if the engine does not move when rolled is the timing chain may have jumped teeth on the cam sprocket. To get to this remove the gas tank, remove all but the rear engine mounting bolts, remove the valve cover. To check remove the fly wheel cover set the piston to Top Dead center, (TDC) on the compression stroke and make sure the mark on the cam sprocket is at the top of the sprocket and not off set.

Good luck.

its to stop the chain from catching onto your clothing & RIPPING YOU OFF IT!
So its not a good idea to remove it!
Also itstops dirt & grime getting all over you & the bike!

Sound like the rear derailer is out of adjustment. Take the bike to you local shop for a tune up.

Turn the adjustment at the shifter while pedaling forward until the chain changes rings and does not jump.

http://www.sansaworldmp3.com/
http://www.sansaworld.com/

It sounds like you have cracked or broken one or both sealed cartridge bearings if thats what your bike has. If it has ball bearings in races they might be broken. Try loosening your rear wheel enough to take the chain off and then turn your crank. See if theres a funny noise or if it feels a little weird when its turning. If you broke a pedal bearing you should be able to tell just by carefully turning each pedal with your fingers and seeing what it feels like. In any case unless you have the tools to repair it you will have to take it in and get it repaired.