+1 to Ken's comments.
Once you get it all on line, I would do one power clean. This is run from the printer LCD and requires raising up the ink levers a few times Whole process takes about 15 minutes.
IF you do this and still have clogs, you can do at least one SSCL (Super Strong cleaning cycle) from the printer control panel, (this is run from your PC/Mac not the LCD of the printer). This process is even more involved but does get most clogs out.
Your biggest issue IMO will be the dampers, as there is no doubt old, and possibly dried up ink in there and as far as I know, no cleaning cycle will get there. However end user replacement of the dampers is not that hard on the 7800 family.
Lastly, make sure you check the wiper. With the power off (make sure it's off), release the head, and manually slide out of the way to the far left. Get a flashlight, and look up into where the head was parked. The wiper is a black rubber device running vertical towards to upper back. Get a swap, foam, with warm water and clean off the wiper. You might also consider a replacement wiper. They are cheap and again can be replaced with a little work. Not as easy as on a 9900, which has a process for it.
Paul C