There are a number of different solutions for your problem.
The easiest solution is to replace the RT31P2 with a switch and connect the cable modem to the WRT54G. This would create one LAN rather than the two LANs that you currently have. This isn't a very good solution though since you would have to replace a component.
Your computers may be able to share files across the different LANs currently, but they just don't see eachother in Network Neighborhood. To test this, use one of the computers to try to access the shares on a computer that is connected to the other router. Rather than going through Network Neighborhood, type in the location of the other computer in the form of "\\ipAddress" such as "\\192.168.1.101". See if you can see across to the other router's systems this way. If this set up works for you, you could actually make links on each machine to point to the systems on the other router. It's not the most elegant solution, but I have seen it work.
Now for a solution that is both elegant and inexpensive (free) but is also more technically involved. This is the best solution I can come up with in your situation. Basically, we will turn your wireless router into nothing more than a switch with a wireless access point. In effect, this will bypass all the router functions -- NAT, firewall, DHCP server, etc -- on the wireless router. This will create one LAN using two routers. The following are the details to implement this.
The first step is to not use the WAN port on the wireless router. All traffic that goes through the WAN port will be firewalled and NATed, which we don't want. We want the wired router to handle all that. Take the cable that is plugged into the WAN port on the wireless router and connect it to one of the standard LAN ports.
Since the wireless router is now just a regular device attached to the wired router, we need to configure it to use the same subnet as the wired router. Use a computer that is directly connected to the wireless router to access its configuration page. Change the wireless router's IP address to one that matches the LAN addressing for the wired router, for example: 192.168.15.2. You should not use an IP address that has a last number greater than 99 since the wired router hands out IP addresses in that range, and you don't want your wireless router to be unable to connect because a computer on the wired router got its designated IP address.
The next step is to turn off the wireless router's DHCP server. You should have the ability to set this in the configuration. You don't want the wireless router to serve as the DHCP server since you want your wired one to handle all of this. After this configuration is made, the wired router will assign IP addresses for every machine, thus connecting every machine to the same LAN.
After you have made all these changes, turn off all the machines that connect to the wireless router, reboot the router, let the router fully boot, and then turn your machines back on. After they have all come back up, make sure that they have a good network connection and can connect to the net. The last thing to check is to see if all the computers can now see themselves.
It's very possible that you will run into trouble if you try to do this. If you do, let us know what you are having a problem with, and we will help you figure out the problem.