Just so you know, Shimano 'Shadow' derailleurs aren't supposed to have a barrell adjuster on the derailleur body.
On top of that, you want to invest $3 in a new cable...
Maybe it's my eyes playing tricks on me, but from those pictures it kind of looks like you've used the same, frayed cable you originally had. You may also wish to look into getting that last bit of outer cable trimmed down a bit. I know when I went from my original, older Deore XT to a newer SLX Shadow, I had to get a shorter bit of outer cable for it too.