The battery went dead in our Apple TV remote and was IMPOSSIBLE to open at the back with a coin. After using multiple tools we got it open to replace the battery
How to replace the battery in your Apple Remote - Apple Support
It should go easy. When was the last time you replaced the battery in this remote? Was the battery still intact? [Old leaking batteries can cause nasty (toxic) chemical reactions.]
and the MENU button no longer works.
All that prying and force may have caused additional malfunction.
I downloaded the Apple TV app on my phone and it searches and cannot find my tv.
Set up the Apple TV Remote app - Apple Support
The iOS device and Apple TV have to be on the same network (same SSID). Some router/modems have separate network names for the 2.4 and 5 GHz band, which would be considered two separate networks.
Try restarting the Apple TV. Try restarting the iOS device.
Linking the app to a 2nd or 3rd generation does require a working remote before app use, to navigate the settings.
ALSO when I plug in the apply tv it goes straight to a black screen and says “could not sign in”
If you updated your Apple ID for Two-Factor Authentication, then you may have to sign in again, with password and verification code. On this device with older software, that makes the login procedure a bit special.
I hooked the Apple TV to my MacBook and iTunes could not find it (tried multiple cords) to restore it.
Restore your Apple TV through iTunes - Apple Support
Remember to also connect the power for this model, as outlined in this support document.
Remember to use a USB cable that supports data transfer (not just a cable for charging purposes).
I even tried to plug it straight into my modem to make sure internet was connected.
That should ease the network setup, but there may be more issues than just that, and it doesn’t do anything for the IR remote.
It seems you have tried a lot already. Let its know if some of these suggestions take you any further.
You can buy a replacement remote from the Apple Store, if needed.
If it turns out that the Apple TV hardware needs service, there are official options. Apple TV Repair - Official Apple Support