ddeand 

UPDATE!

I need to know how to “reset” the right-hand shifter on a 10-speed Ultegra setup that I just got. The shifter has been advanced to the highest setting (big ring on cassette) and will only back off one spot by moving the small lever. I need to get the internal shifter pulley around to where I can insert the cable so the cable end slips into the stop/hole. Does that make sense? So how can I advance the shifter to the appropriate spot if I don’t have the old cable installed in it to pull the pulley into the correct spot? Any suggestions?

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So after trying all the suggestions that you all so kindly recommended, I found that I couldn't get the shifters to work - they were toast. But one of the advantages of being tenacious (or compulsive), plus being retired, I figured I'd give it one more shot. So I started taking the shifter apart - nothing to lose really. After getting the thing stripped down as far as I could, I got my bright little light out to peer into the innards as far as I could go. Lo and behold, I spotted exactly what a number of you had suggested - the end of the cable had broken and was wedged in the bottom of the housing. It took me a while to loosen it and get it out, but I succeeded! The shifter works! Here's what I found as well as the mess I created. I feel pretty good about getting a free set of Ultegra shifters - even though I feel like I re-invented the word angst. Thanks for all the (correct) advice!

shelbyfv

Try holding the large lever stationary while clicking the small.

Andrew R Stewart 

Is all the old cable removed? Does the large lever move with the release one (see shelbfv's reply if so). I suspect that the shifters' internals are becoming gummy from old lube drying out. have you done a solvent cleaning/flushing then relubing, ever? There's dozens of vids and threads on this common subject out there as well as here for your searching.

BTW the usual term for the largest rear cog is the LOWEST gear, as it's the one used when going the slowest. Andy

Le Mechanic

Is the old cable frayed or broken off in the shifter? That will definitely make it difficult to get it to shift to the small cog position to remove/install a new cable. I made a video a year or so ago on a Shimano 10 speed 7900 shifter which is the same process as the Ultegra version that may be helpful.

ddeand 

Thanks for the video - I'll take a look. There is no cable or fragments remaining in the shifter.

ddeand 

Thanks for all the help. The cable has been totally removed and the levers move independently. I flushed with WD40, so we'll see where things are tomorrow. I looked for videos, but apparently was typing in the wrong words for a search. And thanks for the heads up on HIGH/LOW - I always get them confused.

I got the shifters for free and just need to get them working. Fortunately, the cables were still in the other slots.

02Giant 

Insert a cable, keep tension on it with one hand (simulate the derailleur return spring) and operate the shifter with the other hand.

WizardOfBoz

I was gonna say the same thing. IIRC, my experience required something thin you can push with, or a thin hook you can pull with.

ddeand 

Update in first post! Thanks!