None of the parts are showing up for 1.4.4. The interfaces for running out of resources is working perfectly fine. But when I start up the game, it first says that the mod wont work because I am not using 1.4.1, then it says that I placed the mod in the incorrect path.

KSP.log

Correct. TAC LS is functioning absolutely correctly.
You have not installed TAC LS into the correct folder location.
From your log:
C:\Kerbal Space Program\GameData\TacLifeSupport_0.13.9.0\GameData\REPOSoftTech\BackgroundResources\BackgroundResources.dll

TAC LS MUST be installed into the GameData folder correctly.
The correct folder location would be in your case:
C:\Kerbal Space Program\GameData\

Move the folders from C:\Kerbal Space Program\GameData\TacLifeSupport_0.13.9.0\GameData
to:
C:\Kerbal Space Program\GameData\