Well, actually they WERE flashing. I really thought this trusty and very well used printer was on its last leg. Well, it came back from the dead!!! (crossing fingers it lasts).
I Googled the problem and read a few solutions telling me to power it off and on and unplug this and that and my problem seemed to be what others were saying: the printer won't really turn off, the ink cartridges won't come to the center, etc.
I have no idea if THIS is what worked, but something I did made it work again.
With the USB cord unplugged, I held the power button down for about 10 seconds. This time instead of hear a little *tink* like the cartridges tried to engage and initiate the cartridge carriage actually did AND it came to rest in the center when I opened the door (opened door while it was "initializing"). I pulled out all of the cartridges 3 were color ones I replaced just a few days prior and the black was very very low on ink.
After I put the cartridges back in and closed the top I immediately got flashing lights. Again I pressed and held the power button. This resulted in a warning about the black ink being a used cartridge. I decided to replace the cartridge with a new black since I know from previous experience the HP 6500 doesn't like 1 cartridge to be nearly empty.
After replacing the cartridge the print head moved into position, a piece of paper was sucked in and it printed an alignment. Eager to try it out I quickly found something to print.... No flashing lights AND it printed!!!!
Happy day... (hope it lasts & perhaps this little post about the ink helps someone else!)