Um, the auto-quantize feature is probably what is screwing you up. On the transport panel, be sure that the [AQ] button is not lit up during recording....
Dealing w/ MIDI in Cubase is also semi-notorious, because depending on what audio/MIDI interface(s) you are using, Cubase can get really fussy about the driver. I have heard about LOTS of people who have problems w/ Cubase recording MIDI too early. This problem has been discussed at length on the Cubase forum (
www.cubase.net, if I'm remembering correctly)
Hope this helps-