I bought a late 90's Novara Randonee, it came with:

-Shimano RSX brifters
-Shimano RSX front derailleur
-Shimano "Hyperdrive" front triple crankset
-Shimano Alivio rear derailleur
-SRAM 7 speed cassette

[Just as a note, I am very much a novice at bike tuning/repair]

When I picked the bike up, the rear derailleur shifted fine. The front would not shift into the largest chainring, but small and middle shifted fine. The cables and housings all looked original, so I decided to replace them. Install went smoothly, and I was able to adjust the RD properly.

When adjusting the FD, I can't get it to shift off of the smallest chainring. I had taken the FD off and apart to clean it and see how it worked. The FD moves just fine, all the way out.

I re-installed it, and started to adjust it. When I hit the shifter to go up one chainring, it moves over quite a ways, enough to contact and move the chain, but not enough to move the chain to the next chainring.

I set the inside limit as close as it gets, re-adjusted the height of the FD, and
tried rotating the clamp to move the FD closer to the chain. It still won't shift the chain over. I tried the "bow" shifting technique and the derailleur moves all the way out just fine.

So after searching the forum, I am still looking for advice. It looks like some people have said that if your chainrings are very worn, it won't transfer the chain properly. My chainrings look worn, especially the outside 2, but the smallest chainring isn't that bad...

So here's what I know:

shifters work
cables are brand new
housings are brand new
FD is old, original, POS?
chainrings are pretty worn
chain in unknown condition, but most likely very old (replace now or after I get it rideable?)

So should I keep messing with it? Some other trick I probably don't know? Should I just buy a new FD? If so, which kind would work (RSX is obviously no longer around). Buy new chainrings? Does the old chain have anything to do with this? I am going to replace the chain at some point, I just was expecting to be able to ride it after I replaced the housings and cables.

Thanks for any advice, I'm really trying hard to figure this out. I just want to ride it soon, then worry about upgrading components if I feel the need.