Hi,
The 305 error code is a little misleading as it actually refers to a failure of the comprehensive ( Full ) Disk Self Test - this would indicate that the Hard Drive is failing and needs to be replaced and is also consistent with the start-up issue you describe.
If your notebook is brand new, it will be under warranty, so contact HP and arrange to have the drive replaced - if needed, you can check your warranty status Here.
If you live in the US, contact HP Here.
If you are in another part of the world, start Here.
Regards,
DP-K