The "Tattoo" is part of the motherboard... it resides in the BIOS in a section called the "DMI". The "Tattoo" only needs to be done once, provided it is done correctly. If no HP/Compaq logo appears at boot, something is wrong. If you can get the system completely reflashed with overwriting all parts of the BIOS, it should clear up those issues. Then getting it "Tattooed" with the correct system information, should resolve any remaining issues.
HP custome service and authorized facilities will always "Tattoo" the system but have been know to error once in a while. Most likely, the board was flashed incorrectly or with an unauthorized BIOS, or its is a replacement board from an unknown third party.
You should have no issue installing a 1TB drive and no "Tattoo" would need to be done.
Again, no "Tattoo" would need to be done as upgrading to a newer version of Windows doesn't require the "Tattoo" to activate / pre-activate. The only need for the "Tattoo" is when using HP Recovery Discs or an HP OEM SLP factory installed operating system.
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