CRJ50 First Officer reports failure of the nose gear to retract after takeoff; along with associated warnings and cautions. After consultation with Maintenance main gear was extended normally and flight returned to the departure airport for an overweight landing. Nose strut found by Maintenance to be completely collapsed.

Narrative

[We] took off noticing that this airplane seemed to have a rough ride although that didn't seem too unusual. We selected gear up and received a GEAR DISAGREE! Subsequently received the following: NOSE DOOR; warning; WOW [Weight on Wheels] INPUT caution and WOW OUTPUT FAIL status. All gear came up normally except the nose wheel which stayed down and green. Consulted the QRH for gear disagree but realized it applied to a RED GEAR INDICATION which we did not have; we decided that manual extension would not be necessary. We discussed with ATC and were vectored around while we worked on this. We called Maintenance and told them our thoughts regarding the QRH and that we were planning on extending the gear; checking for normal indications and landing. Maintenance agreed. I asked about the overweight situation and was told that as long as actual touch down did not exceed 360 FPM we were ok. Gear came down normally and we landed at 47;600 at about 100 FPM. Returning to gate we noticed that rough ride again. On post-flight inspection I found the nose strut fully compressed which Maintenance said could account for '... all kinds of problems.' If; at any point in the taxi or take off your ride on the nose gear gets rougher; maybe the strut is completely compressed and you will have this problem.