Hi tatemdm,
I understand you have an Officejet L7780 that is having issues with the cartridges. I am sorry to hear this, but I will certainly do my best to help you.
It's possible this is a hardware issue, specifically in the cartridge holding area as it doesn't seem to be holding the cartridges in place anymore. I would recommend that you clean the copper contacts on the cartridges as well as inside the printer (with it unplugged). To do this I would recommend using a Q-tip, as it gives you a bit more reach, and clean the copper contacts on the cartridges (on the end that goes into the printer) and then the contact where that touches within the printer. If this still doesn't work, please make sure you have the printer plugged directly to a wall outlet so that it's getting all the power it needs to function properly.
Hope this helps, but if not get back to me and I will get you a reset to try.