No, don't get a new one. Let's fix this one.
Can you take a picture of the PCB and post it here? If so, can you post a picture that as large and as clear as can be?
Where did you get the "new" battery from? There's a lot of cheap batteries, particularly on eBay, that are new old stock. I've gotten in CR2032s before that where dead when I tested them. Brand new, in the factory package, dead.
You can test batteries with a voltage meter. Get one if you don't already own one, they're cheap enough. It takes the guess work out of this. THIS
is my favorite budget meter. Worth every penny, I highly recommend getting one if you don't already own a meter. I recommend the one in the link, but you can also get ~$10 meters in auto parts and hardware stores. Just be sure to get a digital one that does at least voltage and resistance, and stay away from analog meters.
They're 3v batteries, so they should measure something like 3.2v when they're brand new. Anything less than that and you know it's old stock. And anything under 3 should be considered dead, and you'd want to replace a battery before it hits 3 just to be on the safe side.
The SRAM could possibly be dead. It happens, they only have a certain amount of read/write cycles before they burn out. All memory is like this. If it is dead, it's replaceable. But it's a cross that bridge when you get there situation, you'll wanna rule out all things to do with the battery first. Then you'll wanna test the SRAM theory.