Unplugging the router will NOT set it to defaults.
If your kids, or you, did NOT figure out the necessary user name and/or password to get into the router's configuration settings to access the configuration settings, then your kids, or you, could not have set the router settings to defaults that way.
If your kids, or you, did NOT use a stiff wire or similar in the proper hole to press on the reset switch inside the router case for x seconds, then the router was not set to defaults that way.
If you, or your kids, did none of those things, something else was / is wrong.
"Product: Lynksys router / Wrt5rg v4 "
You made at least one typo. There is no such model !
Is it WRT54RG V4 ? - note the 4 after 5
Did you buy it in the US or Canada ?
If yes to both, the main manual has lots of mentions of "Save settings" buttons.
To be sure the settings are saved
- use a network cable between the router and the computer you're accessing the router with's wired network card.
- make sure both end connectors are all the way into the ports.
Both end connectors should "latch" into the network ports, such that they will not pull out unless you press the lever on the end connectors.
The cable sheath should not be pulled out of the end connectors.
People often break or fatigue the lever on the end connectors, which makes it easy for the connector to move out of the port and have a poor connection, or pull out the cable sheath out of the end connector, which makes it easier to damage any of the connections of the 8 wires at the connector.
If that doesn't help, use a different network cable.
If that doesn't help, your router is damaged. Get another router.
What password were you setting ?
Were you changing the password to get into the router's configuration ?
You can do that if you like, but that has nothing to do with your problem, and you may forget the password eventually and have to reset the router's configuration to defaults externally by using a stiff wire or similar to press on the reset switch. .
Were you setting a password for the encryption in the security settings?
You don't have to do that - all you had to do was copy down the password, and use that in Windows when you want to Connect to the router to change the security settings for your wireless network adapter.