Front Derailleur/Shifter Problem

[kazz]

I'm brand new to bike maintenance, and I have incredible difficulty getting my front derailleur to shift into the third (highest) gear, and then staying there. I don't know if the problem is with the shifter or the derailleur, and I would really appreciate any help.

derailleur: shimano (that's all I know about it)
shifter: a cheapy gradient thumb-knob shifter. No clicks, no numbers, just a - and +
[EDIT: after some further reading, I discovered the more accurate term is "friction" shifter.]

Problem: as I move the shifter up, it becomes increasingly stiff toward the high gear. I can usually crank it all the way up until the derailleur moves the chain to the highest gear, but then once I let go of the knob, the derailleur bounces back to the second gear.

Here's what I've done so far:
- checked that the derailleur was between 1 - 2mm above the biggest cog and parallel to the chain
- replaced entire cable and housing (housing was cracked anyway)
- adjusted the high limit screw until it fell out (I put it back in, of course, but left it really loose)
- adjusted the cable tension (see below)

I adjusted the cable tension several times, but it didn't correct the problem. When I loosened it part way, the only difference was that I could move the knob a little higher on the shifter before it started getting stiff, but it was still just as hard to move the derailleur all they way over. When I loosened it significantly, of course, there wasn't enough tension to move the derailleur at all.

I also took apart the shifter and it didn't appear that anything was broken, but I've never seen the inside of a [friction] shifter before, so I don't know if anything was wrong with it.

If anyone has any advice, I'd really appreciate it. Thanks.