While you can certainly connect devices to the WRT54GL in router/AP mode, that just creates a separate network, essentially an island that has no access to the rest of the world (i.e., your network and the Internet). You need to wirelessly “bridge” the WRT54GL router to the Netgear DG834G modem/router.
The traditional means to wirelessly bridge devices is called WDS, and both devices would need to support it. And since WDS is not a certified wifi protocol, implementations vary across manufacturers, so incompatibilities are common. But assuming each supports WDS (they probably do), you could still try it. Just don't be surprised if it doesn't work.
The better solution (and one that would definitely work) would be to install dd-wrt (third party firmware) on the Linksys WRT54GL and configure it as a “repeater bridge”. Fortunately the WRT54GL, versions 1.0 and 1.1, support it. Now all your devices, regardless of which router you use, are part of the same network and have full access to any other devices and the Internet.