"Local Only" - run out of sessions?

[#1]

We run a Computer Learning Centre on Tuesday mornings for the elderly.
12 PCs running mostly XP and a couple Vista connecting wirelessly via an ancient Intel PRO/Wireless 2011B LAN Access Point and an old Netgear Router (not sure of model).
At start of morning all machines access internet OK.
As some clients come in with their own machines we try to add a few more laptops (usually running Vista) to our network.  These later additions can access the local network (printers, shared folders etc) but NOT the Internet.  They show "Local Only" when hovering over wireless connection in System Area.
If we restart the Router, these new laptops showing "Local Only" are able to connect to the Internet so the laptop settings must be OK.  But some of the other (older) machines display a reluctance to access the Internet.
Have we run out of "virtual circuits" or sessions or something like them?
No fixed IP address - we let DHCP take care of all that.
No wireless security - we use the mains power switch to prevent unauthorised access!
This has been going on for several months now and we are stumped.  Have thought of buying a new wireless router but our funds are low so don't want to waste money when a simple parameter change would fix the problem.
All suggestions appreciated.
Brian

[#2]

Well what is your dhcp scope? Sounds like you have run out of leases.
You may need to go into the router setup, and change the default lease time to something like 30 minutes instead of the 7 days or what ever it is currently. That and/or increase the amount of leases used, i.e. if the range is 192.168.1.100-> 192.168.1.120 then ONLY 20 machines can be connected. Be aware than ALL off the items on your network will need an ip address, so if you do extend it make sure you allow for printers etc, or if they have static ip's that you don't include their address in the range.