This post should help you out on the issue, they did a very good job on explaining it too. iPhone 7 home button not working after screen replacement In my view you may have damaged something when you replaced the battery. You should take the device apart again and see if you put the ribbon cable in correctly.
You need to possibly replace the screen, it sounds like one of them has gone bad. Nintendo does not repair these devices anymore so you may need to take this in your own hands and try fixing it yourself. You could try finding a place for repairs but they may charge a bit more.
From what your saying, It sounds like you may need to boot into GM9 (Godmode 9) and possibly restore the NAND backup you did. You could try booting into the 3DS Update Recovery mode, which is by holding A+R+L+Up and powering it on. If that fails and you have no nand backup, try updating your Luma version.
Rubbing alcohol will do the trick! Just get a Q-Tip and clean the contacts of the cartridge! You could try cleaning the game card port but be cautious about it. The best way to clean that is with a can of compressed air to blow all the dust and stuff.
The device is water damaged. You should follow iFixit’s guide on repairing the device with water damage. Be careful when using it through, if there is water on the battery, IMMEDIATELY remove the battery. Electronics Water Damage
You may need a new battery. Batteries tend to wear over time, that could be the problem. You could also try removing the battery and with the battery out, hold the power button for 10 seconds, put the battery back in and check.