Can shift gears,but bike wont move.I am able to shift in and out of gears,but cant get the bike to move.Have adjusted the cable in and out,and it does'nt seem to matter.

Loosen the handle bar adjustment a lot, .then take a little slack out of the cable at the engine connection, then re-adjust the handlebar lever with a bout 1/8" play

sounds like your shift lever may have been put back on in a different spot on the shift shaft. make sure it can move up and down with out hitting anything.

When was the last time you replaced your cables?
If you have checked that every other part of the drive train is free from obstruction (eg. move the front deralieur with your fingers) then I would strongly suggest looking at your cabling. Once new cable are fitted then you can adjust the limit screws on you deraileurs to get your gear shifting nice and smooth. YouTube is full of useful videos.
Good luck!

worn shifting fork,,,located under sidecase where shift lever is located,,or possibley stretched clutch cable,,not totally dissengageing,,,adjust cable,,,usually wont shift when off unless you rock bike back and forth.

Set the rear derailleur to the lowest gear (big cog) and the front to the lowest gear (small chain ring). Disconnect the derailleur cable. Screw in the adjuster for the cable tension all the way (this adjuster is on the shifter of a mountain bike or the down tube of a road bike). Pedal to make sure the chain is not rubbing on the derailleur cage. If it is, adjust the "L" setting on the derailleur until the chain moves by without touching the cage. Now pull taut and reattch the cable and shift the front to the big ring while pedaling. If it does not shift up well or completely, hold the shifter past its normal shift and adjust the "H" screw so that the derailleur allows the shift. Shift into the highest cassette gear and keep pedaling. The chain should not be touching the front derailleur's cage when you pedal. Adjust with the barrel adjuster until the chain moves freely without touching the derailleur cage.

i hope this helps
-matthew

Wash, degrease and scrub the chain and derailleurs with a good degreaser (like Simple Green). Dry the chain and relubricate it with an appropriate bike chain lubricant (not oil or WD-40). Shift the derailleurs to the smallest chain ring and cog on the cassette (low front gear, high rear gear) and then loosen the cable at the derailleurs, pull the cables taut and reattach them. If the derailleurs still need adjustment, here is a procedure for it:
Flip the bike over (so you can pedal the bike manually while you shift) and shift the front to the middle chain ring. Shift the rear to the highest gear (small cog). Release the cable from the pinch bolt on the derailleur. Adjust the screw marked "H" on the derailleur until the jockey wheel on the derailleur is aligned perfectly over the small cassette cog. Set the cable adjuster on the derailleur to the middle of its range (find this by screwing it all the way in and then count how many revolutions it makes until it screws out completely. Screw it back in one half of the total revolutions). Reattach the cable and shift to the lowest gear (the biggest cog). Over-shift and hold on the shifter, then adjust the "L" screw on the derailleur until the jockey wheel sits just past the last cog. You have to hold the shifter to do this. Now shift into the middle gear (or one of the two middle gears if the bike has an even number of gears) and adjust the derailleur using the barrel adjuster you previously set to the middle of its range. Adjust it so that the derailleur is sitting perfectly over the appropriate gear. Shift up and down the cassette while pedaling and in every gear, reverse pedal (freewheel) to make sure the chain does not hop. Adjust as necessary until all gears are smooth.
Now the front:
Set the rear derailleur to the lowest gear (big cog) and the front to the lowest gear (small chain ring). Disconnect the derailleur cable. Screw in the adjuster for the cable tension all the way (this adjuster is on the shifter of a mountain bike or the down tube of a road bike). Pedal to make sure the chain is not rubbing on the derailleur cage. If it is, adjust the "L" setting on the derailleur until the chain moves by without touching the cage. Now pull taut and reattch the cable and shift the front to the big ring while pedaling. If it does not shift up well or completely, hold the shifter past its normal shift and adjust the "H" screw so that the derailleur allows the shift. Shift into the highest cassette gear and keep pedaling. The chain should not be touching the front derailleur's cage when you pedal. Adjust with the barrel adjuster until the chain moves freely without touching the derailleur cage.
That should be it, unless there is another mechanical problem causing the missed shifts, like a bent derailleur hanger or damaged teeth on the cassette cogs or a bad derailleur. If it is still problematic, come back for further information.

i hope this helps
-matthew

There should be one or two limiting screws for the front derailleur that you can use to adjust how far out/in the derailleur moves to shift the chain over. You can ask a friend to lift the back end of the bike off the ground while you do the adjusting of these screws and then try shifting the gear while moving the peddles with your other hand.

There are good instructions here under front and rear derailleur adjustments:http://www.parktool.com/repair/byregion.asp?catid=53 This is my favourite site:http://sheldonbrown.com/gearing/index.html Hope this helps.

I do a lot of mountain bike riding and there have been a few times where the gear changing hardware has definitely become bent rendering it nearly useless when it comes to changing gears.  Inspect the hardware very closely for any signs of damage.  Also be sure to look at where the gear shift cables meet the gear shifters on the bars.  Where it connects in you will typically find an adjustment knob (note that you may have the same type of adjustment knob where the cable meets the gear shift mechanism also) which the cable rides in.  You will make much larger jumps in adjustment when using this method as the screws on the gear changing mechanism, which you mention in your original post, are more for fine tuning.  Best of luck to you on te repair and I hope you don't need any new hardware!
Joe

It sounds like the limit screws on the derailleur are out of adjustment.  If the derailleur cant pobbible move any farther towards the 3rd gear and the cable has slack in it then we know for a fact that the limit screws are to blame.  
If you can move the derailleur with your hand past the 3rd gear then we know the cable needs to be adjusted.  I would recommend taking it to a bike shop as those index shifters do take a bit of work to adjust correctly.