Ralf,
I just got my HD44780 based 16 x 1 going and ran into the same problem as
you, in my rookie opinion your problem is  the initialization (assuming no
wiring probs), I made extensive use of web pages:

http://www.iaehv.nl/users/pouweha/lcd2.htm#PIC_example    <-there is a
diagram for the wiring
and
http://hobbes.king.ac.uk/matt/pic/lcd.html

(Thanks to Peer and Matt for these educational pages) you will probably have
to make a few changes to suit your setup (there is info there for 2 line
displays) but the code here works good,  make sure your  pinouts match your
software assignments for those pins,
good luck
 -Russ
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>I want to drive an LCD Display (16x2) with a PIC in 8 Bit Mode (see
>Microchips AN 587). I used a 16c84 not an 16c74 like Microchip in AN 587
>and assembled the Circuit. If I switch on the Power, only the upper Line
>of the Display is black. I guess the Initalisation or the Wiring between
>PIC and Display is wrong.
>Can anybody help me?
>Thanks
>Ralf