I've had a motorcycle sitting for 10 years. How should I get it running again?

When it stopped running,the problem was it would not start, the rest of it worked although needed some fixing. Like brakes, new tires and the chrome was faded.
I have taken it to a shop that said it might be about $2000 to fix. Similar bikes (Honda Shadow 1100 1985) run about $2500 still with the same amount of miles 24,000 so I have no reason to buy one when the dealer said the work down to the heads that leak oil would be about $2000.
The only problem could be the carburetor if they can't rebuild it. What would you do?
No answers like trash it,I have too many good times on this bike to do that if it can be fixed up the the price offered.

Like Johnny says, the biggest factor is going to be labor.
Parts are still around. About 2 years ago, I bought a head gasket and o-rings for an '82 from the dealer. If your carbs are too far gone to be rebuilt (doubt that), then there are re-buildable ones around.
My source for old Honda parts: http://mcsalvage.com/

I would shop e-bay or junk yards, there are several..
for some new carbs....they can be troublesome to
rebuild.. not impossible, but a headache....
bleed some new brake fluid in and change oil....
worth it too...

get the manual and it will pretty much tell you how to pull the bike apart and put it back together again.

If the carbs can't be rebuilt, is there an alternate fit? If you can be assured of carburation, and your heart is set on keeping the bike, your answer is clear.

Used parts all over for it rebuild what you can and replace the rest -Shop time is the big factor in that kind of thing @ $55 to$90 an hr

I have a bike on my lift right now that hasnt ran in over 20 yrs and thats my plan. 76 Shovel with 12000 actual miles

First thing :

1.track down a new carb rebuild kit.

2.Change oil.

3.Empty old gas if any, remove tank and clean out with new gas, just to rinse it out.

4.replace all fuel line.

5.replace points & cond. if it has them. + spark plugs need R&R.

6.Fill with gas and see if it starts, then work from there on the rest of the bike.

7.Set the carb. by using vaccume gages.

This should get you running again. If not, your very close.

well sounds like you got a good fixer, as long as the motors not seized,
i work on old bikes all the time, the one im curently rehabing was left out side for the last 7 yrs uncoverd, but the motor still kicked over with a little finness, so i draged it home shot a lil either in the carbs and it fired for a second. so i pulled the carbs cleaned thouroly, thru in new plugs, fyld the points now it starts with a couple kicks every time,
so check the carbs your-self, chances are you can rebuild them, then change the oil, drain the tank, clean the petcock, make sure gas runs out it with no problem, clean the points, put in some new plugs with the rite gap, maybe have the valves checked for the rite clearence, and you should be good to go.

Buy a gasket set on EBay, and spend a couple of quality weekends with your motorcycle cleaning out the carburetors, cleaning and gapping the spark plugs, putting a small amount of lube into the top of the cylinders through the spark plug hole, charging the battery, ...