Indeed the problem sounds like it is the need for pullups on the P0 pins.

I did a 3 digit LCD drive of similar ilk a while back and had to equip the P0 lines with 10K ohm resistors. On the general flavor of an 8051/8052 the P0 lines operate in true open drain mode when the port is used for simple port I/O. The pullups will give you the ability to have full logic level swings on these pins and your LCD would probably start to work.

MICHAEL KARAS