Rear derailleur shifting

Today was a day of firsts: first day to change shifting cables, first day to (almost correctly) adjust my derailleurs. Also, in case this is part of the problem, I put on a new chain/cassette combo. Overall I'm pretty happy with the result, but there's one issue I just can't figure out: rear derailleur cable tension (at least I think that's the issue). Either it's loose and I have poor indexing, but can shift to all the gears in my cassette or it's tight and I have wonderful shifting for 9 out of 10 sprockets, but can't shift to the innermost/largest one (even after playing with the L screw). Actually, I can 'shift' to my largest sprocket by pulling the cable by hand, I just can't shift into that gear using my shifter. I'm obviously missing something, I just don't know what ... any thoughts?

My first guess would be that the cable is way loose. If you can shift it by pulling it manually then you're probably just a full step too loose. Have you tried just taking out more slack in the cable? It should be taut when you're in your small cog.

Another possibility is that it's hanging up somewhere. Did you replace the housings, or only the cables? Does the cable pull smoothly through the housings?

Did you change gearing, or just put on a new cassette with the same gears? You shouldn't have to touch the L or H screws, but if you changed your low gear, you'll need to tweak the B screw.

I'd put the L screw back where it was, actually ... especially if you took your pie plate off. You don't want the chain going into the spokes.

I would second Oak's advice, but would like to ask another couple of questions. You mentioned that you changed the cables, did you replace the housing as well? Often times the housing that feeds into the rear derailleur will show these same problems. I also might wonder if you looked at the dropout; I have to assume that it is straight? Lastly, how old is your rear derailleur? Try this to answer that question: have your chain in the smallest cog on your rear wheel, take the derailleur and push it so that it is now on the lowest/biggest cog and let the derailleur go (all without using the shifters). If your derailleur pops back to the original cog, then the spring tension is fine... if not, then the derailleur needs to be replaced.

When replacing a cable (shifting or brake),
1) Turn the cable tensioner in all the way so that it isn't putting any additional tension on the cable.
2) While using pliers on the end of the new cable to pull it as taut as possible, fasten the screw that holds the cable in place.
3) Finally, use the tension adjuster to get the cable taut enough to shift to all the gears.

My rear derailleur was working fine up to the point when my shifting cable snapped. I don't think it needs to be replaced (although I'll try ridebikeme's test later today).
Yes, I changed the cable housing too (cut to the same length as the old housing).
I did change gearing in the cassette from an 11-28 to 12-27 but haven't really touched the B screw yet 'cause I'm not entirely clear on what it does.
It's possible that my cable's too loose, but I've tried to get it as tight as I can. Is there a trick to this?

Thanks Hi Ho Silver - I had been keeping my tensioner in a neutral/middle setting so I would be able to tighten or loosen if needed. I'll try again with it completely loose.

How did you cut the housing ... did you make sure to remove all burrs from the ends? if you have ferrules or barrel adjusters, is the housing inserted firmly with no wobble? is the ball end well seated in the shifter? Are you certain the housings are correctly routed?

The B screw aligns the derailleur body to move the top jockey wheel toward/away from the cassette. In your biggest cog there should only be a small amount of clearance. Still, one tooth smaller shouldn't keep it from shifting without an adjustment, just might be a little noisy. Same with chain length.

I cut the housing with electrical cable snips. I reshaped the ends after the cut, but did not look for or remove burrs. I'm pretty confident that the housing's routed correctly and seated well in the shifter - the barrel adjuster's worth a 2nd check, but I think that's alright too.

It was just too loose. I completely loosened the barrel adjuster and reattached the rear derailleur cable. My chain hopped onto the largest cog after a little tightening of the adjuster. A friend also told me about a 3rd hand tool - she claims it makes this process much easier.