Birch beer not carbonating

I made a 5 gallong batch of the Gnome autumn red birch beer awhile back for the kids and for some reason, I can't seem to get to carbonate. I've had 45 pounds on it at 35 degrees F for over 2 weeks and it's just not going anywhere. I have a full tank of CO2 and I even tested it so I know that not the problem and I know the corny is not leaking either as I tested that too. This is my first attempt at soda and I do live at 6600 feet. Could elevation be the issue?

Elevation won't make much of a difference. How much head space do you have in the keg and did you purge it before carbonating? Head space is important because CO2 adsorption rate depends on the surface exposed to CO2.

For future reference if you carbonate the water first and then several days later add the other ingredients (chilled) you will have better success with carbing.

Ahh, good tip. As for headspace, there is probably about 4 inches so not a whole lot really. Should I dump some do y'all think?

No. Shake it for a few minutes (with the gas connected). Check the carbonation level. Repeat until it's carbonated.