It sounds like the L brifter was not "zeroed out" when you loaded the cable. It's a commonly overlooked issue, even with experienced wrenches (you get busy, you are in a hurry, and doo doo happens....)
1-Run the small L brifter lever "in" a few times. Try to pull on the L cable while you do so.
2-Pull the L brake lever down, and look to see if the cable end is easily seen and would come right out if you pushed the cable backwards.
No matter what you see, do this:
3-Remove the chain from the FD. sometimes you just unscrew the back of the FD and slip it out.
4-Remove the cable from the FD and let it sit loose.
5-Pull the L STI housing away from the L brifter.
6-Pull the L brake lever, and try to push the L shifter cable back out of the brifter, so you can get a grip on the end. If you can't, it was inserted before the shifter was all the way down. Even if you can, it's better to start from scratch.
7-Pull out the cable.
8-With the cable out, keep shifting the L small lever "in" until it won't click. Then shift the big lever "in" the same way.
9-Repeat about 10 times, minimum. You should get good play. The 8-sp DA and 8-sp 600/Ultegra should both act smoothly.
10-Now, shift the L small lever "in" until it won't shift any more.
11-Pull down on the brake lever, and look into the cable feed hole from the outside. You should get a clear shot at re-feeding the cable.
12-Re-feed the cable, route it through the housing, stops, under the BB and up towards the FD.
13-STOP. "Zero out" the small L lever again. You need to make sure when you feed and clamp that cable, it's all the way released.
14-With the chain off the front rings (usually resting on the BB), do your adjustments on the FD. No chain, no cable connected.
15-Re-attach the cable to the FD. Before you tighten it, make sure, again, the small L lever is zeroed out. Can't be too sure.
16-Tighten the cable. Ease the chain back into the FD.
17-Nine of ten times, you hit that L big shifter now, three times, and you'll throw the chain over the outside of the big ring. That's good.
Adjust the FD and ride.
I honestly don't know what else to do. I've seen lots of L brifters with the cable inserted and tightened before it was zeroed down.
Worst case scenario, the cable bends and kinks inside the brifter.
Send it to cudak888 and he'll use the big wrench on it.
Bad cases make it almost impossible to push the cable back out, and you may have to cut it off and work out the end piece.
Mild cases let you push it out, with almost no clearance. These are more common.
Always better to take the extra 5 minutes and go from scratch. Shortcut the cable, shortcircuit the shifting.
Same thing happens to R brifters all the time. Sometimes the brifters are zeroed out, but not fully, and they ease back a click while you're finger-doodling the cable, derailleur, etc. Always stop and make sure the shifter is zeroed out, with full cable extension.
Upon review, Jim beat me to it.
PS: It's a great way to pick up a set of "non-working" 8-sp STI's for cheap. The seller is often very frustrated and glad to part with them. I always offer to fix them, then buy them if I can't. 8-sp STI's are simply limited in what's generally wrong: a) gunk b) cable insertion as above c) return spring not seated. Most of the time, you fix those, you're good.
Live your life like Coleman did.
1985 Raleigh Racing USA - Competition
1984/85/86? Klein Performance
1988 Centurion Dave Scott Ironman Master
1989 Centurion Dave Scott Ironman Expert
1989 Centurion Carbon R