Unable to login with my normal username & password after crash

About a week ago, I got a "service battery" notification, after I let the battery discharge completely.

The other night, the system abruptly shut down while running on battery power, at 40% remaining charge.

I plugged the power adapter in, waited for the battery to recharge, and attempted to re-boot: it took over an hour.

When I did get the login screen to display, I noticed that my user picture was missing, and I am unable to login using my username/password, as if my user profile has been deleted. Also, the system beachballs at the login screen, while attempting to enter data, or while using the trackpad. I see no option for logging in as a new user.

I have reset the PRAM, and attempted to restart in Safe Mode, but still experience the same problem. I ran Disk First Aid and everything checks out fine...I replaced the HD about a month ago, and it should be ok.

I am now thinking about re-installing the OS, however, I ordered a new battery that will arrive day after tomorrow: Should I wait, and install the new battery BEFORE attempting to reinstall the system software? Or, should I just try to reinstall now?

Could the battery itself be the root of these problems?

Any advice is much appreciated...thanks in advance!