HP Deskjet printer buying guide

I have the printer said above and it is not working. I have called HP and they will not talk to me because warranty is done and their website is not helping out either.
The problem with the printer is that the power light, return (paper) light, and both ink cartridge lights are blinking. In exactly that order and not all at once. Not only that but the ink cartridge goes to the left side of the computer (where the lights are) and just sits there. I was hoping that someone could somehow help walk me through what to do to fix my printer.
The things I have done to the printer to try to fix is what the website tells me…turn off the power (which it actually will not turn off unless unplugged), and/or unplug the power cord from the wall and/or printer, and I have cleaned the strip that the ink cartridges slide on with an alcohol pad. Which none worked and those are the only options I could find for the problem.
And just one last thing to remember….I cannot use the power button to turn off the printer.
Any help would be greatly appreciated. Thanks!