first off, you can't check a starter with a meter unless you know the resistance specs, which even manuals don't give.
second, if you jumped the solenoid terminals and the bike stared, then the wiring to and from the solenoid is fine, and so is the starter. check to make sure you have a 12v signal to the solenoid when you hit the start button. if not, there's your problem. it could be a bad start switch on the bars, or depending on the bike, a bad kickstand safety switch, or a bad clutch safetly switch. to disconnect either of the safety switches, unplug them and jump the leads. if that doesn't work, check the wire from the starter switch to the solenoid, and make sure there's 12 (+) to the start switch itself. easy way to check it is to take apart the right bar switch set, use a meter to make sure one side of the switch has 12v (+) with the key on. if it doesn't, you need to run a new switched lead to the right bar controls. if it does, put the meter on the other side of the switch and make sure you get 12v(+) when you hit the button. if you get 12v when the button is pushed, then the problem is in the wiring between the switch and the solenoid. if you don't then the switch itself is bad or has dirty contacts. (happens alot more than you'd think)
you can just check for continuity between the switch and a switched 12(+) source (with the key on), and for continuity between the other side of the switch and the soleniod (doesn't matter if the key is on for that one)
basically, the path of electrisity is like this :
battery (+) - into harness to right bar controls (into start switch)- out of switch, back into harness - to solenoid signal point.
that signal is all that tells the solenoid to close and let juice flow to the solenoid. without it, you gets nada.
what kind of bike is it? i have manuals for every single jap bike known to man (for the most part) on my computer, and i can get you OEM color codes to look for, if it helps.
here, i even drew you a picture. it's pretty staright forward, but ileft out the clutch and sidestand switches. if the bike is in nuetral, these won't even matter.
oh, one more thing, did you make sure there's 30a fuse in the new solenoid, inder the electrical plug? if you replaced the solenoid, but didn't put a fuse in it, you get NOTHING, no lights, no nothing. that is the main fuse for the bike. check that first, simple mistake, and seeing as how you had lights before but none after the solenoid swap, it'd be a good bet there,s no fuse in there.