Why will my led not light up & why does my input voltage fluctuate when I add a wire?
I think you may have wired it up wrong. It looks to me like you did this:







simulate this circuit &ndash; Schematic created using CircuitLab

I think you want this:







simulate this circuit

Pull the end of the purple jumper off of pin 3 and move it to your \$+15\:\textrm{V}\$ rail.



Below is a piece of your schematic and some information I've added. The arrow points to a "cross-over" and NOT to a connection. Just in case that helps.





Your newly added picture does appear to show a shorted LED. However, your first picture does not appear to show a shorted LED. I wouldn't have been able to tell from when I was reading your post, because your last picture wasn't added by then. Now, looking at it it does appear that it could be shorted out. Did you move it between pictures???

Anyway, that is another detail to look at and double-check. I think you already know (knew) that all five holes along a row are all connected together. That's a detail that everyone needs to know just to use a protoboard. So I assume you are aware of that. But anyone can accidentally get a lead in the wrong hole, too. So it's worth checking out just to make sure.

Best wishes here.