Congratulations on your free HP1000. Something is always better than nothing.
Hard to say if there is something wrong with the SSD. If you can post the full and exact error message that might help. However, on gut instinct it sounds like the drive might be faulty.
It might be worth getting a distribution that can be booted from a USB stick and using that to check the drive for errors. If the drive is faulty then the choices are buy another one (never that cheap for SSD) or learn how to install and run linux from a usb stick.
As for the battery, bin it. Either buy a replacement or run the laptop off the mains. Life's too short to be killed by you're own computer.
Sorry, possibly not what you wanted to here. But with a little ingenuity there's no reason you can't use it.