Recently, my trunk is not opening when my car is off. It sounds like it's trying to open but it won't. As soon as I turn the car on then it will open. It's acting like it needs more battery just to open. Please help!

 

Welcome to the site..

If you have no cranking speed issues, or similar door lock/unlock problems, Id be suspect of the trunk release solenoid ..

 

Ok, I am not having any other lock problems. Is the release solenoid the part where the trunk releases and closes? It almost looks like a hook?

 

Its part of the lift gate latch. The trim panel would need to be removed to gain access.
Unless the latch is bound (debris etc), it would seem it would be weak, more so if with the engine running (more available voltage) the op is then normal..
OE battery?