I had some problem compiling EQ2 and also to start. And after some try I found how to do it correct...at least for me it worked. If any body has the same problem I hope this will work.
How to compile EQ 2.
1 Download zlib source code and copy it to the hard drive.
2 Use Visual Studio 2003, go to tools options, then to Project and then to VC++ Directory.
3 go to Include files, and past this in to it....C:\Program Files\MySQL\MySQL Server
5.0\include and the same for Zlib...C:\zlib123
4 then go to liberay files and past this in to it....C:\Program Files\MySQL\MySQL Server
5.0\lib\opt
5 download the Zlib.dll compiled version and rename zlibwapi.dll to Zlib.dll and copy it in
to your EQ 2 emu folder.
And start the world.exe
If you are not compiling the source but download the compiled EQ 2 and you get the zlib.dll error.
Just download the compiled zlib.dll and put it in your EQ 2 Emu folder and rename the zlibl.dll to zlib.dll if it has a different name.

I believe this thread also has the exact same information:
http://eq2emulator.net/forums/viewtopic.php?t=100

Which states:

Note: Building off of Ash's post because this is very useful.
Original Resource: http://www.eq2emulator.net/forums/viewtopic.php?t=99