After taking off, the landing gear handle remained latched 'down' when the nosewheel did not center. The flightcrew then used the nose gear steering override switch and turned the nosewheel until the 'off center light' extinguished. The override switch was placed 'off' and the landing gear latch retracted, but when the gear handle was raised, the landing gear remained down. The override switch was tried again, but to no avail. Approximately 5 to 10 seconds later, the landing gear retracted. During arrival at the destination, the nose gear came out of the 'up position' when the gear handle was lowered, but a 'down & locked' indication was not attained. The 'off center light' illuminated again and the gear handle latched down. The nose gear steering was turned 90 degrees left and the gear became stuck. Attempts to recenter the nosewheel and/or get a safe indication were unsuccessful. During the landing, the nose gear collapsed. An exam of the nose gear revealed that the steering slide assembly, PN 27-423031-17, was bent.