Hello and welcome to JustAnswer!
The door should open with the mechanical key no matter what. If the key turns and feels normal then most likely that problem is with the door latch. If you don't feel any resistance when you turn it then the linkage between the lock cylinder and the latch could be off.
It's possible that the fob portion of the key has failed and that's the reason you can't get in by pressing the unlock button. I see that it's been a while since you posted your question, if you still haven't been able to get in and are wanting to repair it on your own the first thing I'd recommend is having the fob tested to see if it's sending a signal. This can be done for free at many larger parts stores like Autozone.
You may end up having to enter the car using a lockout kit to move the door frame open enough to get a tool in and pull on the door handle, or a slim jim type of tool to go in through the window glass area and try to unlock it that way. If the linkage between the lock cylinder and latch is off or the latch itself has failed then a slim jim wouldn't work.
Thanks for the comprehensive answer. I'm pretty sure the car battery is dead, not the fob. Is there any way to pop the hood from the outside so i could hook some cables up and attempt to jump the battery? I would rather avoid using a lockout kit if i could.