I regret hearing that the printer has had such a problem.
I think that there is a tendency to clog, obstinately, in the inking system.
Soaking the print heads was a good measure to try - provided that you never touched the metallic contacts on it while handling it, nor ever touched the inky underside where the ink 'nozzles' are. That would have ruined the print head, requiring it to be replaced. (Please let me know if you think that is what happened.)
If the clogging is elsewhere in the inking system, or owing to some other cause than the print head being removed owing to being touched wrongly, then this might help:
1. Clean the (colored) print head. (Not by hand, but by the menu function in the Setup or Settings menu on your printer, possibly under a 'Maintenance' sub-menu.)
2. Wait 1/2 hour to several hours or overnight, leaving the printer On but unused (no print jobs, etc.)
This allows waste ink to soak into the print head and hopefully dissolve dried ink etc.
3. Clean the print head a second time.
4. Wait again (as in step 2 above) for 1/2 hr. to several hrs., printer On but unused.
5. Clean the print head a third time.
Then test whether colo ink is showing up at all in prints at this point. If it is, even faintly, then repeating this procedure will (eventually, at the cost of a certain amount of ink wasted in the process) clear up the clogged print head.
After that fails, if it does fail, what you need to do is to decide whether replacing the print head (which may cost something considerable, more than you would think usually) is better, given the printer's age, or whether it would be more preferable for you to replace the printer altogether with a new one (and hopefully recycle the old printer, always a good idea.)
So try the triple-cleaning-with-wait-times that I recommended, and get back to me if it doesn't work for you (so I can advise you further...)... or if it does help (- I always like to hear that something I recommended has worked!)