Is my problem the internet signal or the wireless router?

CONTINUAL DISCONNECTION OF WIRELESS CONNECTION
There are a few things thatcan cause you to lose wireless connection with your wireless router.1. Weak signal strength,check the signal strength on your wireless card. If it is weak move thewireless router away from brick or concrete walls and if possible locatethe wireless router higher up.2. Have you secured yourwireless router from people near your from unauthorized access? i.e. change thedefault password, setup encryption use WPA2 or WPA, change the default SSID,and turn off SSID broadcast, and for added protection, enable MAC addressfiltering which allows only the MAC address/es of your wireless card/s toconnect to your wireless router.3. You could be gettinginterference from electrical sources such as air conditioners, arc welders,washing machines etc. If so, the power supply to the wireless routers andcomputers etc should be connected to a surge protection power board, betterstill connect your computer equipment to an UPS (Uninterrupted PowerSupply). 4. Check the channels ofthe wireless routers and access points in your area and change the broadcastchannel on your wireless router to an unused channel or one that is currentlyused but has the weakest signal strength. This will minimize interferencewith your wireless router from other wireless routers and accesspoints in your area.

The most common solution for this is to disconnect/unplug the power supplies from both the internet modem and the router, they may be one and the same, then wait a full minute or two then plug them back in. The power should now be recycled and back to working status. Restart your computer so it grabs a new IP address. If this doesn't work then call your Internet Service Provider (ISP) and have them help you confirm signal from their end. They may send you another router or help change the proprietary settings.
TF

It can take up to 2-5 minutes before your router starts broadcasting a wireless signal and for the xbox to be able to connect to it, turn your xbox off and the router wait a minute then turn your wireless router on, wait a further few minutes and turn your xbox on and try using the wireless connection

You can reset both the modem and the router by removing the power cord where it connects into the router (Called Recycling the Power) I would do it with both the modem and the router for about a full 2 minutes.
Sounds more like you have a connectivity issue from interference from something on you desk. Some known culprits are:
High Intensity Lamps Fans Radio Interference coming from your wireless phone Power strip with filters for telephone signal any other environmental issues including computer monitor. Next door neighbor's router signal bleeding through. Filter device missing from phone Filter device missing from phone line connected to you TV
Try moving the router back to the old location. Does problem go away. You are now too close to something thats breaking your signal. I can log into my neighbors access point across the street and two houses away. Signals are strong but can be blocked by a lot of things mentioned above or tin foil.
Check it out,
TF

1.Log into router. Using either 192.168.0.1 to 192.168.1.1 in a browser window that is ( internet Explorer or Firefox)
2. Verify wireless router name( on the computer) >>> ( on/off) ( router status window)
3.Note router name you are connecting to.
4.. Check the laptop do ipconfig /all to see current IP addresses.
5. Set the laptop up in the router by WEP KEY or MAC address. This set up in the "security tab" in the router. using 192.168.0.1 or 192.168.1.1 to access through a browser.
6.Note router name you are connecting to.
7. Move the laptop about 20ft away and try to log on to the internet.
This is for all routers to set up wirelessly.
8. check for firmware update at the manufacturers site for your model router
9. cell phones, cordless phones, digital TV's, can affect the data signal from a router. Also distance from the router can be a factor. If your router is in a basement place the router to a upper floor and center it in the room.
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Recommend that you go one step at a time.

1) unplug the wireless router.
2) reset your Cable modem or DSL modem. Wait until the lights show the Wide area network or WAN is working correctly before applying power to the Netgear wireless router.

3) After a minute or so, its signals should change from amber to bright green.

Repeat if necessary. If this doesn't provide the connectivity that you need, a call to your Internet Service provider may be necessary.

Please check the following

1) secure cable between modem and router. it must not be loose.
2) secure cable between modem and phone jack. it must not be loose.
3) modem and router must not be near to any electromagnetic devices such as halogen lamps, computer speakers
4) cables must not be intersecting to electrical cable which sometimes cause static signals that interrupts internet signals going to modem or router

The wired connection is working.

You are not able to go online when it is wireless.

Check if the computer is connected to the wireless network ?

If it is not connected to the wireless network then you will need to connect to the wireless network.
you can also check the wireless settings of the router.

Click Here for more info about wireless connection

The cable internet is not "seeing" the computer. The router is blocking it. That is why it works if you plug it into the modem directly. How to solve this is to turn everything off and unplug power to modems and routers for 3-5 minutes. Then replug in routers. Then restart computers.

That is why it worked at the computer store. Everything was shut down and restarted.

Also, sometimes it is necessary to call the ISP (for example Comcast) and have them re-send the signal. Also going to Control Panel Network Connections and choose "repair the connection" will reset the signal.
Be patient it will work.

maybe you should try to purchase a better wireless adapter,like dlink dwa-110