Very weak wireless connection on Debian live image install

Question

I'm having a problem with the wireless connection on a fresh install of Debian 7.4 which I didn't have before, I had Debian installed before and WiFi was working great, the only thing that changed this time is installing it from a live install image instead of the CD/DVD images.

My wireless card is Atheros AR5005G, and ath5k is already installed.

I'm trying to fix this problem and I searched about the issue but everything I found was about increasing txpower using iwconfig or setting power to off which is already off in my case.

So what could be the problem:

• I remember that it was working fine on an old Debian distribution which had the madwifi driver
• I'm dual booting Debian with Windows and on windows it's working fine
• My laptop connects to the router without any problems
• I had a live USB using the same image which had the same problem
• I didn't have this problem before when I installed from the regular CD/DVD images
• I have to be very close to the router to be able to access the internet
• Pinging the router or any website takes a long time with many lost packets
• 408 (Request Timeout) errors occur while browsing

Running lspci -v shows:

0a:03.0 Ethernet controller: Atheros Communications Inc. AR2413/AR2414 Wireless Network Adapter [AR5005G(S) 802.11bg] (rev 01)
    Subsystem: AMBIT Microsystem Corp. Device 0418
    Flags: bus master, medium devsel, latency 168, IRQ 18
    Memory at d0000000 (32-bit, non-prefetchable) [size=64K]
    Capabilities: [44] Power Management version 2
    Kernel driver in use: ath5k

Update:

Here are the dmesg related messages:

...
[7.485709] ath5k 0000:0a:03.0: registered as 'phy0'
...
[8.429871] ieee80211 phy0: Selected rate control algorithm 'minstrel_ht'
[8.430578] ath5k phy0: Atheros AR2413 chip found (MAC: 0x78, PHY: 0x45)

And this is the full output of dmesg on pastebin.