Can state of chicken affect brine?
How do you 'notice' when the brine hasn't reached certain areas?    

Its easy to see if the brine is working and you're possibly just overcooking - weigh the bird pre and post brine, before cooking.  If it weighs more, you've got the liquid.

A properly brined bird shouldn't taste like 'omg, thats salty!'.  I think two things are going on here:


Your expectations may be off.  Brining isn't magic.  It just gives you more liquid in the bird so that when you cook some out there's more at the end.  (It can enhance flavor if you add herbs &amp; spices to the brine also).
You may just be overcooking the chicken.  If you overcook it enough, the brine will appear to have done nothing - you've just cooked out all the juiciness you put it.  Use a meat thermometer and make sure its 'just right'.  


Brining definitely works though, and it shouldn't be overly bird specific.