Rocky,
Can you please answer all the relevant question in Posting Guidelines at the top of this forum? That will help us run down your issue quickly.
The log file is located here: <workspace folder>/.metadata/.log
What driver are you using to connect to Sybase, are you sure your connect string is correct, can you paste it here please?
Also, have you managed to connect to the database from the same machine outside MyEclipse? (Java program or command line tool, etc.)
I looked up JZ00L and it looks like you could have a problem with your username, password or you are being refused a connection to the database for some other reason (max connection limit, open cursors, etc.).
If possible, you could try restarting the database and see if you can connect to it.
Best,
Brian.