One trick that has worked for a number of people over the years is to put Windex (the type with ammonia in it) on the parking pad and let the head sit in that for several hours. On most desktop units, getting to the parking pad is most easily done by hitting the ink change button and pulling the plug to cut power to the printer when the head assembly moves aside. Flood the parking pad with Windex. Then manually move the head back to the parked position. Don't plug in the machine for several hours. Windex can hurt the interior seals of a head, but people have allowed heads to sit in this Windex overnight without problems.
A Windex soaked cloth strip like a bias tape pulled back and forth under the head can also dislodge stuff stuck to the bottom of the head.
All that said, if two channels have trouble at the same time, it could be that the pump has failed. Once that happens, cleaning is ineffective and nothing but a new pump will cure the problem.
Good luck.
Paul
www.PaulRoark.com