Do you know what you did to bring the console to that 8046 bluescreens of death error?
Have a look at TurdPooCharger's signature for flashcart options. Note that you will need any other working DS system to flash a cheap cart into ntrboot mode while the R4i Gold 3DS Plus comes preflashed and has an internal switch for ntrboot/DS game modes.
A hardmod is dangerous if you are not skilled/good with the soldering iron and the hardmod is less helpful than ntrboot. You would need to have a good, full NAND image in order to repair the damage while ntrboot can start GodMode9 for troubleshooting in any case.
Any attempt to flash an image via hardmod should be done after backing up the current bricked status. There might be console unique data that could be lost in case anything with flashing via hardmod goes wrong.
Good luck!