My linksys router doesnt have a default gateway and the reset buttton on the router doesnt work either

Check the IP address on your computer.
Connect the computer to the router and check the IP address and default gateway on your computer.
The default gateway is the IP address of your router.
If it is 192.168.1.1 then try to open the setup page. Power cycle the router and see if that works.

See How to open 192.168.1.1

I think you should reset the router and reconfigure it.
If the wired computer is also not working then I think you need to reconfigure it for sure.

See How to reset Linksys router.

Watch.
How to setup Linksys router without CD.

On older LinkSys routers, the default username is blank and the default password is "admin." On newer Linksys routers, both the default username and the default password are set to "admin." If that doesnt work, there is a small hole on the back of the router with a reset switch. Press it with a pointy object for about 20 seconds and it will reset the router to default settings.

You can reset the Linksys back to the default settings by -
Power up the Linksys and press and hold the pinhole RESET button at the back of the Linksys for approx. 30 secs until the router reboots, then release the RESET button.
Connect a LAN cable from the LAN port on your computer to the Linksys router. Open a browser and enter the Linksys' configuration URL.
http://192.168.1.1
The default login = admin
The default PW = admin

To secure your wireless network from unauthorized access,please click on this link and follow my instructions :- http://www.fixya.com/support/r3559128-wireless_router_security

" 401 unauthorized" authorization required " .This message means the user name and password for the router is not correct. the default password of the Linksys router is admin with no user name ( leave it blank )
If the default password is not working then the router password must be changed.
If you don't know the password of the router then you will need to reset and reconfigure the router.
Once you reset the router , it will come back to the factory default settings.
Click here for more info about router and network

that num is the default dns num for a linksys or netgear router. reset your router and it should work. unplug the router and the modem and wait a few min and plug in. if this doesnt work. look for the reset button on the router and stick a pen point in it with the power on. you will see all the lights blink out, then let go of the reset button and it should go back to defaults.

ok
check on back side of router then u see reset button press it for 10 seconds then it restart and also reset all settigns to defaults.then u have to reconfigure it,
u cna access your router with one of the following lionk
http://192.168.1.1
or http://192.168.0.1
type useranme as "admin" and pasword as "admin" or blank

http://www.coderetard.com/2008/05/30/install-dd-wrt-firmware-on-linksys-wrt150n-wrt160n-wireless-routers/

Probably need a firmware update.

so you can access the internet by getting connected by LAN cable. so now try to open the router by its default ip and look for the wireless securities setting and reconfigure them properly and if you are not able to access the router than there is reset button which reset the router to company default. and once you have reset the router than you have to configure it again as per your requirement.

The following is not a solution but a set of steps to determine an issue. Wire the router back up -- connect a computer to it using a wire -- can it access the internet? If so the WAN side router config is fine. The issue appears to be a wireless issue. Did the wireless card lose the proper configuration settings to access the router? Did the wireless adapter disconnect and need to be reconnected?

If nothing above was an issue we need to do some other testing -- I do not believe this is likely in this scenario where things were working -- but as we have not yet found out a cause.

Turn all machines on before the test and do not turn off until after

On at least one wired computer that is working and one wireless computer attaching to the linksys router I want you to do the following

Click Start then All Programs then Accessories then Command Prompt

In the window that opens type

ipconfig /all

press enter then record all of the following for each adapter

• adapter
  
• IP address
• Subnet Mask
• Default Gateway
• one or more DNS addresses

The back in the window enter the following command using the default gateway from the wired connection (your router address)

ping 192.168.1.1

you will either get 4 timeouts -- the connection fails or 4 messages with elapsed times generally measured in ms or milliseconds.

What you are looking for in the above
Good entries base
u should be unique for the linksys network
Wired IP address 192.168.1.u
SubNet Mask ?.?.?.? assuming 255.255.255.0
Default Gateway 192.168.1.1
DNS addresses ?.?.?.? not 0.0.0.0
where at least one is not zero.

Then wireless entries should be
Wired IP address 192.168.1.u should be 192.168.1.u
SubNet Mask same as wired
Default Gateway same as wired
DNS addresses same as wired
If these are wrong there is a configuration error either in the router or wireless adapters depending on how you want your network setup.

each connected adapter wired and each wireless should also
successfully ping the default gateway or router address

If the ipconfig is right and the wired config has successful pings, then every wireless adapter that fails has a wireless config issue.

If you are willing to work through this let me know and reply with information in a comment to this issue.