Okay. Does the printer have any flashing LED lights on it? Like is the power button flashing or cancel button flashing? Unforunately, I'm not terribly familiar with printers as old as yours since I'm relatively new to HP. I think you only have 2 buttons from what I've seen in the picture.
If you open the ink access door, does the carriage move to the middle so you can put in new cartridges? With the printer turned off, can you move the carriage freely?
You could try resetting the printer. I'm not quite sure how to do a hard reset on the older printers, but this post says
To do a hard reset:
1. Make sure the printer is on.
2. Pull the power cord from the printer.
3. Pull the power cord from the wall.
4. Wait 30 seconds.
5. Plug the printer in and turn it on.