HP 4630 Black Ink Cartridge Problem rejects new cartridges

[TOC_Jonah]

This HP OfficeJet 4630 worked just fine for a long time, until a new  Genuine HP Black 61XL cartridge was accidentally installed by someone else without removing the tape over the printhead and the electrical contacts on that brand new Black cartridge.  The only indication of any printer problem was that the display said that it was "printing in single cartridge mode" as if it was the only cartridge present in the printer.  That meant that black and white documents were printed using only the color cartridge. When the color cartridge no longer printed darkly, I checked the Black 61XL print cartridge and discovered that it still had the factory-installed  tape over the printhead and the electrical contacts.  When I removed that tape and reinstalled that cartridge, the display then read "Ink Cartridge(s) Problem. The following Ink Cartridge(s) must be replaced." and it showed a bowtie symbol >< to indicate the Black Cartridge was the one to be replaced.  At that point the 4630 printer froze and would not respond in any way to any controls.  If I left the printer turned on and removed the Black 61XL cartridge, the printer display would again read "Printing in single cartridge mode" and would print documents.  I tried installing a brand new Genuine HP Black 61XL cartridge, but the printer immediately froze again with the exact same display reading "Ink Cartridge(s) Problem, The following Ink Cartridge(s) must be replaced." and it showed a bowtie symbol ><" notice rejecting the brand new HP 61 XL cartridge.  I have replaced the HP Genuine Color HP 61XL cartridge, but that only allows the 4630 printer to print more nicely in Single Cartridge mode if the Black 61XL cartridge is completely removed from the printer.  There is more than one caution I have seen  that the 4630 OfficeJet printer should not be turned off without cartridges in it, or the printer might be damaged.  I have updated the firmware today for this printer, and that has not helped.  I am reluctant to continue to buy new HP 61XL cartridges if they will not help. I hope that the printer was not damaged by having that factory tape over the Black cartridge, but with the printer being frozen and unresponsive with a Black cartridge installed, I don't know how to proceed.  If the printer now has a hardware problem requiring repair, it is likely to be thrown away.  Please help me if you can. Thank you.