MacBook Pro Suddenly Shutting Off

I am experiencing my MacBook Pro shutting off randomly. The battery can have a significant charge but will shut down at about 30 minutes of use. When I turn it back on it will keep shutting back off right after I log in. Everything works fine when I have the laptop charging. I have already tried Safe Boot, SMC Reset, PRAM reset, installing a new OSX profile, and using First Aid from Disk Utilities. The battery menu says the battery is normal and I pressed D when I booted up to run a test and there were no hardware issues. I bought a new battery to replace the one I have now but I need to try to fix this problem in the meantime since I can't charge my laptop all the time at school. Is this a hardware issue for sure or is it a software problem?