Two things, Pamela - I would definitely cut off those stems above where they are turning yellowish, then maybe try rooting one of the plants by sticking in a pot of damp potting soil and keeping just barely damp. The foliage you have on those cuttings still looks fine. I don't think the length of the cutting should matter. The roots will form at the leaf nodes IF they form. (sometimes it's just the wrong time of year, and some things just insist on dying instead of rooting) You could also try cutting a few inches of your longest stem off, and just lay it horizontally on some moist potting soil. Some things root that way very well, too.
Second thing, you should never root cuttings in a narrow-necked bottle like that. Choose a wider mouth jar or vase, so you don't break your tender little roots when you need to pull the cuttings out of there. Some things make big, long roots quite quickly and it's agonizing to have to pull them out of a bottle, breaking your hard-earned roots as you go.
You're so right about the anti-depressant value of plants, but please keep your perspective and know that sometimes they do just die and it's not your fault.
One lady who posts on here often had a saying at the bottom of her posts "Gardening is my therapy, and I'm in therapy a lot".
