If the shifter was very old, I'd think this might be one approach:
https://www.youtube.com/watch?v=9657OoOY3oE

Given that it's not that old, I'm less inclined to think that'll help.

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http://www.jt10000.com/

what type of front shifter are you using? Most tri bike shifters (shimano and microshift) are friction shifters for the front derailleur except RTC shifters so there is no "click". You definetely do not want the big ring limit screw set too far where your derailleur can throw the chain off the ring- you want it so the outside of the derailleur plate is about 1mm from the chain.

When you say you cant shift because of the lack of a "click" what do you mean exactly? can you shift the chain up to the big ring at all or will it just not stay? A few things to check is 1) recheck the limit screws by taking the cable off the derailleur and re-setting the small ring first (1mm from the inside of the derailleur plate to the chain) 2) re-attach the cable as tight as you can get it without moving the derailleur 3) re-set the big ring limit screw as noted before. Also make sure your shifter assembly screw is tight (screw on the side of your shifter that controls the mechanism tension) because if it is too loose it wont be able to hold the cable tension.

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Andy Mullen
Team Zoot

I have shimano shifters. When I shift down to the small chain ring, I hear a click and I can't move it any further. Currently when I shift up, there is no click, so I can move the shifter up, all the way past where it moves onto the big chain ring and dumps the chain. When I first got the bike, when I shifted up, there was a click and I couldn't move the shifter any further upwards. Whereas now, when I shift up, there is no click and the chain dumps. The biggest issue is when I turn the high limit screw the derailleur doesn't move. So I might try what you said and take off the cable and reset.

the click is the just the maximum distance click on shimano shifters- you dont need to get it to click when going up to the big ring as its a friction shifter. Just make sure the shifter screw is tight enough to hold the chain tension when in the big ring.

The maximum range of travel on the upshift with a friction shifter is set by the limit screws as all front derailleurs are slightly different. Turning the upper limit screw in (clockwise) will move the derailleur inward towards the bike and if it bottoms out before you derailleur is close enough to the big ring check the lower limit screws again.

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Andy Mullen
Team Zoot

I had a similar problem a few weeks ago on my Speed Concept with SRAM shifters. Basically, whenever I shifted up to the big ring as soon as I took my hand off the shifters it would fall back to the small chainring. It drove me nuts adjusting and resetting the limit screws on the front derailleur. Then I looked at the shifter itself and realized that was where the problem was. These friction shifters are extremely low tech. The front shifter moves through an arc that pulls the cable into the big ring or the small ring. The only thing that hold the shifter in place through the arc is the tightness of the screws in the shifter, hence friction shifters. I tightened the Allen screw on the shifter and my problem was solved. Not sure this is the same problem as you have but I hope it helps somehow.

I am not sure what the technical term is, but there is a bolt that serves as the axis for your pedals and runs through the bottom bracket. Last year I had a similar problem, thought it was my shifting, but it turned out the bolt was just loose and the pedals were moving side to side. it took less than five minutes for a mechanic to fix it, and he did not charge me.

This is what you do:
1) Undo cable at front der.
2) set the lower limit screw so the inner side of the der cage (the one closest to the seatpost) is almost touching the chain when in smallest chainring up front and the largest cog in the back
3) Attach der cable to front der, holding it under tension while tightening the bolt. When bolt is tight the cable should have good tension but not have caused the der to move.
4) CAREFULLY shift up to the large chainring and shift the rear cogs to the smallest cog.
5) adjust the outer limit screw so outer side of the der cage is about 1 mm or less from chain (ie. not quite rubbing).
6) Try shifting the front chainrings up and down. If it does not go up to large chainring easily, you need more tension on the der cable. If it won't drop down to smallest chainring, you probably have a bit too much tenion.

The screws only set the limit of the der path of movement. It is the tension on the der cable that determines how far the der moves WITHIN that path of movement.

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"Oh man, it's going to take days to kill all these people!" - Jens Voigt

After trying to adjust the derailleur and resetting the gears, I decided to take it into a mechanic. Turns our the crank was loose and coming off. This looseness caused the gears to move out of place and the derailleur couldn't move far enough to make the shift. Once the crank was tightened a couple minor tweaks to the limit screws and she is up and running again.