Do you need to change your Cobra Remote Battery?
All Cobra remote controls take one CR2032 Battery. I recommend changing your Cobra remote battery after about 3 years, but if your remote has stopped responding, or the range has dropped then you can do a simple test to see if the battery is still good.
The following video shows how to check if your battery is good in your Vodafone Automotive/Cobra alarm remote. Not that the test is the same for the Padlock style remote.
This test also works on the 2 button padlock remote as well as the 3 button padlock remote.

Cobra Padlock Remote and G Series Remote (Same remote just different cases)
Opening the remote
The Padlock remote has a couple of small slots which a small flat blade screwdriver can fit in to prize the remote open:

Use a small flat blade screw diver to open

Work it open from both ends
I find the G series Remote is easy to open by running your fingernails around the edge of the case.

The G Series remote found with the AK4698 can be opened with your fingernails.
Once opened the battery is easy to access. All remote controls take a CR2032.
I keep replacement cases both of the G series and the Padlock remote. If you want to change which style case you then the internals are transferable. Cases are $25.00 each.