Rear mech problem - won't shift gears

Hi all,
The rear mech on my son's Hoy 20" bike seems to have gone. It started by not being able to move the chain up to the first gear. Now it won't move it up or down at all. I can push the mech up to slacken the chain, but I don't think it's moving in or out.
Does anyone know what might be wrong and if it's a simple fix? If it's more complicated, do you know roughly how much it should cost to get it fixed by a LBS? My LBS is currently shut and the nearest one that's open, let's just say I'd like to have an idea of what it should cost.
Many thanks in advance!
Josh
The rear mech on my son's Hoy 20" bike seems to have gone. It started by not being able to move the chain up to the first gear. Now it won't move it up or down at all. I can push the mech up to slacken the chain, but I don't think it's moving in or out.
Does anyone know what might be wrong and if it's a simple fix? If it's more complicated, do you know roughly how much it should cost to get it fixed by a LBS? My LBS is currently shut and the nearest one that's open, let's just say I'd like to have an idea of what it should cost.
Many thanks in advance!
Josh
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Have a look at Park Tools website for their guide on re-aligning a rear mech, see how far you get if you dare otherwise it's a LBS job.
Bottom line - if you can't fix it yourself then you'll have to pay whatever the LBS want to charge you. Hopefully a decent LBS will only charge you for the labour as long as all the parts are good to go.
Trek Fuel EX8 '09
Bike shops are very busy right now fixing all the bikes that have been left at the back of the garage for the last 12 months.
With the cable inner free, hold it with some pliers and apply slight pressure (pull on it). Shift the shifter to see if the cable moves in and out as expected. Go through all the gears. If it moves freely, the chances are either the hanger is bent and/or the indexing and end stop adjustments need setting up properly.
If the inner doesn’t move correctly or freely, I would remove the inner and inspect it looking for frayed strands etc. You will have to replace it with a new one if you remove it but they are very cheap. Can you inspect the shifter to ensure it operates correctly?
I’d try a new cable inner first and make sure the hanger isn’t bent. If the new inner still doesn’t move freely I would fit a new outer and ferrules. Assuming the hanger is straight (you can’t tell exactly by eye alone, but you will see a badly bent one), then fit the new inner and outer if appropriate. Follow the derailleur’s set up instructions to check end stops and then clamp the cable and index the gears.
If they still don’t work it is likely a problem with the shifter which may, or may not be repairable.
PP