Why can't my iPhone 4 can't find Wi-Fi?

Okay, so my brother had an old iPhone 4 that was broken (screen cracked, home & lock button don't work, etc). He got it fixed for $140 and gave it to me and now its working brand new. However there's one problem. My iPhone can't find any wi-fi unless it is close to the router. For example, the router to my house is in my room, I can only use my internet's wi-fi on my phone in that area, I can't use it in my living or in my sister's room or in the kitchen. It's the same everywhere else. I have to be near the router to access wi-fi otherwise my phone goes to 3G internet. I don't ALWAYS want to use 3G because it wastes my data plan. Please someone help me. There has to be a reason for this. It will mean a lot.

Thank you.

P.S It's an iPhone 4, White, 16GB with iOS 6.1.3

Local area Wi-Fi® network information is needed to complete several steps.

From the home screen, select Settings.
Select Wi-Fi®.
Drag the switch right to enable Wi-Fi®.
***
Join an existing Wi-Fi® network
From Choose a Network, select an available network. Select the name of the network, not the blue arrow.
Enter the username and password then select Join.
***
Add a Wi-Fi® network
When re-adding a Wi-Fi® network or if a network setting is in need of correction, it is recommended to remove the Wi-Fi® network first. Refer to Remove Wi-Fi® Connection - Apple iPhone 4 for assistance.
From Choose a Network, select Other.
Enter the Wi-Fi® network name.
Select Security.
Select the Wi-Fi® network type then select Other Network.
WEP
WPA
WPA2
WPA Enterprise
WPA2 Enterprise
Enter the Wi-Fi® network password then select Join.
***…
FOR a DEMO watch this…

***…
Please refer to the network administrator for additional assistance.