Remote key triggering alarm

Hi. I've got quite a weird problem here, and need help with this ASAP as my alarm is going off constantly in public. It looks like I'm trying to break into my own car!

I drive a 2001 Passat, 1.8
Yesterday I replaced the battery in my remote key, after it being dead for about a year. I went to use the key, and all the remote functions worked perfectly! Doors locked and unlocked, and trunk popped open as well. No reprogramming was needed. Everything seemed to be in tip top shape.

Later that night, after about 3 hours since I had last driven the car, parked and locked it, I went to unlock it with the remote. Instantly the alarm was triggered, and I could not get it to stop unless I inserted the key into the door, and manually unlocked the car. I did this, got inside, shut the door and the alarm started again. This time I got it to stop by placing the key in the ignition and starting the engine. All the while I am trying the remote functions of unlocking the doors as well as the panic button, and the car was completely unresponsive to this.

When I had driven to my destination, I got out to lock the car only to trigger the alarm once again! Finally I got the alarm to stop by manually locking the car.

I find it odd that the remote key was working perfectly earlier in the day, and now it seems to have gone haywire, or in need of reprogramming. Does any have an idea of what I need to do? Thank you!

EDIT: Also, I forgot to mention that while the alarm is going off, the red LED light on the remote key is blinking constantly.