Bad news first - I'm not actually certain the TOS of Experts Exchange allows us to help you here - you've just told us you (mis?)use free trials for commercial use. Not having a trial EULA for SQL Anywhere in front of me I'm not sure if it prohibits commercial use. If so then what you've done is piracy and stealing from Sybase. Even if the trials are allowed for commercial use it's a bit... shabby of you that you keep downloading trials rather than paying for software you clearly are using to make money. The licenses are expensive. You should buy one.
Open up a hex editor on the .DB file, there might be a header that tells you the version. I think you either have a very recent release (12?) or a very ancient vintage (6 or earlier), if 10 and 11 can't deal with it.
Also to correct a mistake you seem to be making - the ODBC drivers are not what's letting you connect to the .DB file. This is not like a .PDF or .RTF which can be read by many programs; the .DB file is the area of disk storage used by a database engine, and only that database engine can meaningfully read it. The only thing you can do with the SQL Anywhere ODBC file(s) is to talk to the SQL Anywhere engine, and that is what's reading your .DB file for you.
Hence my statements above, you are not just "installing the ODBC driver", you are installing an application that requires a paid license and using it to do work that is commercially valuable to you.
Whatever the version of .DB file you have, you will also have to install the full SQL Anywhere database engine of the correct vintage. Do please think about paying for it this time.