Chosen Solution

MacAir 11’‘ Late 2010 with a bulging battery (keyboard puffed up). Charger cord shows a green light. It powers on with the charger, but I get only a lighted LCD screen with a slash-circle at its middle that periodically alternates with the Apple logo. Doesn’t go to boot at all. Is it safe to remove the battery and operate the laptop without that battery? I’m hoping the logicboard and SSD are still OK. I’d buy a replacement battery only if I see everything else works fine.

Oh Boy! You got a few issues. Yes your system can boot up without the battery. You’ll need to take the battery out and disconnect the charger. Press the power button for a minute to drain the logic. Once thats done plug the MagSafe back in you should be able to boot un now. But! You appear to have a second problem which is then getting it the way! Your SSD does not have a workable OS on it as you are seeing the Prohibitory symbol About the screens your Mac displays as it starts up Lets try this restart the system this time and press the Option (⌥) to get to the Startup Manager. Do you see a valid OS present? If you do select it and your system should boot up. If not you’ll need to boot up from either an external bootable drive or leverage Internet Recovery (this time pressing the Command (⌘) and R keys) to then create a bootable external drive so you can then try to fix your internal drive. Mac startup key combinations

Update: I removed the bloated battery but still can’t boot from the SSD. It’s probably corrupted. So I booted from the USB stick I had for late 2010 Mac Airs and formatted the main drive (Mac OS Journalled). I tried to restore the OS (using Disk Utilities) from the hidden partition containing the factory disk image in it but still no joy. I ended up installing the original Snow Leopard OS from the USB stick into the main partition and now everything works.