Bad news, I'm afraid. The only program which will open an AppleWorks database is Appleworks. Though Word Processing documents can be opened in Pages, and Spreadsheets in Numbers (and Draw documents in one version of EazyDraw), nothing whatever will open an AppleWorks database.
The only possibility for retrieving it is to find a way of running AppleWorks - for example if your Mac will run Snow Leopard (i.e. if you upgraded it from that and didn't buy it with a later system ready installed) you could install Snow Leopard and AppleWorks on an external hard disk and boot from that.
If you can do that you can export the database as ASCII text and import it into Bento or FileMaker Pro (or other databases) but you will lose all formatting and calculation fields will bring over the result, not the calculation.
More information here: http://www.wilmut.webspace.virginmedia.com/notes/aw/page5.html