Is the earth (I think you call 'em "ground" in the US) wire good off the starter? Considering the juice the starter takes, I'm amazed that wire isn't thicker, it doesn't look up to the job to me, should you ever need to crank for more than several turns!
Another surprise is that the pos (main battery supply) terminal onto the solinoid is just exposed, no plastic protection cap! Easy to drop a spanner down and short out onto the frame. (I covered mine, very nearly caught it a few times, especially when bolting up headers etc).
I have a few ideas I'd personally try, may help you?
Is the new solinoid good, not sticking? If it's clicking then your key on is good. Have you tryed keep turning the key, as if keep going to start, worth a try keep "clicking" it on, and it may just eventually turn over??
? Try rocking car by pushing back and forwards a foot or so while in gear (with no one in it; it will be hard to budge).
I probably shouldn't suggest it, but if all your wires are good to the starter unit / terminals tight / battery fully charged, and no joy with other suggestions, then personally I'd give the starter a wack, as in hit down on to it hard with a short, sharp blow from the blunt end of a metal bar, while someones trying to start it.