My iPhone 4 won't connect to Wi-Fi unless I'm standing next to a router?

I just bought an iPhone 4 (ios 6) from a guy and when I got it, everything works perfectly fine except for the Wi-Fi. My iphone won't connect to Wi-Fi unless I'm standing next to my wireless router (located in the living room) and when I walk to my room, I lose signal and then the internet won't work anymore. I have an ipod touch too, and the Wi-Fi works just fine (its 4 bars when i go to my room ) my laptops work fine too. It's just my iphone that doesn't work. How can I fix it? I can't get the iphone replaced because I don't have a warranty and I didn't buy it from the Apple store.

What I'm thinking is wrong with it is it's internal antenna is messed up. Possibly trying making a call? If the call works successfully with very little problem then I doubt it's the antenna. Other than that, I'm not to sure, sorry.

You got robbed

Depending on what the problem is:
If he had taken apart the iPhone he would've not re-plugged in the antennae inside the iPhone
The only reason I could see him taking it apart is to replace a broken screen
Other possibility
Could be a software issue. I would to try this first, look up how to enter DFU (direct firmware upgrade) mode and update in iTunes to re-flash the phone software and that may fix the problem

--- Edit ---

The phone and Wi-Fi antennae are separate