Charles, has this combination worked previously, have you been able to print from your Dell Dimension 2400 to your HP Deskjet 3070A successfully?
If the answer to the above is Yes, then if you believe that the printer is still working correctly and you can test this with a different computer able to print to it, you should consider uninstalling and re-installing the HP software and device drivers for this printer.
If you have not printed to this printer successfully previously, have you tested the printer with a different computer and proven it is still working fine?
If the printer works fine to a different computer then providing you are using the same USB cable to connect to your Dell 2400, the problem needs to be narrowed down further.
Check that you can plus other USB devices into the port on the Dell used for the HP printer - if these work, then your USB port is good - if not, try another port if you have one.
If your USB hardware is good, then again you are left with the need to uninstall and re-install the HP software and device drivers - it may be worth trying to download the latest version of such software
if available. HP tend to update their All-in-One software on a regular basis.