Lcd's power up in 1 line only, the top one, if you disconnect the data lines power one up and turn the contrast all the way up only the top line will go black, I use this to tell if a processor has started or not.
If you are getting data displayed on the top line not the bottom the display must not have initialized correctly, if the display works with these 4 lines floating and not with them grounded then that's pretty much certain to be causing the problem.
You can save yourself a pin, the r/w pin can be directly grounded if you dont read from the Lcd, which isnt really necessary in a lot of projects.