Is the problem that the second monitor shows when Windows loads but otherwise not during the boot process? If so, that's not uncommon. It can create difficulties if trying to boot external media. There is sometime a setting in the BIOS that might help (tho accessing the BIOS in this situation can also be a problem).
If you specifically need the second monitor available during POST/BIOS, check the HP BIOS for settings such as Primary Display, Video/Graphics, Multi-Display, or IGD/Discrete Graphics.