my Acura mdx 2005 remote key doesn't open the door.
I would change the battery in the keyfob first and see if that works.
The simplest thing to do is to change the batteries in your remote.
It's the cheapest solution, so let's start from there.
If that doesn't solve the issue, we need to check if there is a problem with the remote key or the sensor in the car. This can be a bit tricky.
However, you can never buy a new remote with an old car sensor. At the end, you will need to change the whole system.
So start with the batteries in the remote, after that check the wiring and circuit of the whole system. Maybe there is a fault.