Wifi connection works but can't connect to internet

Question

I've recently switched to using Slackware 14 on my laptop, so far I'm quite happy with the distro, except for 1 really annoying little thing: I can surf using hotspots, and all sorts of public wifi-access-points, but I can't seem to get on-line at home.

Prior to running Slackware, I was using Debian, so yes, my laptop has been on my home network, without mac-spoofing or anything.
Currently, I've setup my wlan interface as eth1, and added these lines in my /etc/rc.d/rc.local:

wpa_supplicant -B -Dwext -ieth1 -c/etc/wpa_supplicant.conf

Which does the trick, it seems, using something like wpa_cli or wpa_gui, I can easily connect to my home network.
I therefore changed the wpa_supplicant file a bit, adding:

network={
    ssid="HomeSweetHome"
    psk=0123464sdasd4d56agr6 #output from wpa_passpharse HomeSweetHome mypassphrase
    key_mgmt=WPA2-PSK #and so on
}

But no matter what I do (use settings above, or connect manually) I can connect to other machines on the LAN, but as soon as I try to google something, nothing happens. Constantly "Waiting for siteX" is all I get.

Does anybody here have any idea as to what I'm missing here? There has to be something I haven't configured as supposed to here... I can't think of anything ATM, though.

Update:

Yes, I can ping 8.8.8.8, no problem. I can add network locations and share files with the other computers in the network, too.

Output of ifconfig eth1:

eth1: flags=4163<UP,BROADCAST,RUNNING,MULTICAST>  mtu 1500
        inet 192.168.1.64  netmask 255.255.255.0  broadcast 192.168.1.255
        inet6 fe80::213:ceff:fef1:5267  prefixlen 64  scopeid 0x20<link>
        ether 00:13:ce:f1:52:67  txqueuelen 1000  (Ethernet)
        RX packets 491  bytes 57950 (56.5 KiB)
        RX errors 0  dropped 0  overruns 0  frame 0
        TX packets 75  bytes 10228 (9.9 KiB)
        TX errors 0  dropped 0 overruns 0  carrier 0  collisions 0
        device interrupt 17  base 0x6000  memory 0xdfcff000-dfcfffff  

Output of route -n:

Kernel IP routing table
Destination     Gateway         Genmask         Flags Metric Ref    Use Iface
0.0.0.0         192.168.1.1     0.0.0.0         UG    303    0        0 eth1
127.0.0.0       0.0.0.0         255.0.0.0       U     0      0        0 lo
192.168.1.0     0.0.0.0         255.255.255.0   U     303    0        0 eth1

ping google.com: All went well, 0% packet loss, on average 20ms/packet.

tcptraceroute isn't installed at the moment, but I'll set it up in due time. For now, here's the output of traceroute -n 8.8.8.8

traceroute 8.8.8.8 (8.8.8.8), 30 hops max, 60 byte packets
 1  192.168.1.1  1.190 ms  1.872 ms  5.465ms
 2  192.168.0.1  5.520 ms  5.699 ms  6.960 ms
 3  78.21.0.1  15.007 ms  15.850 ms  17.525 ms
 4  * * * *
 5  213.224.253.9  27.151 ms  28.096 ms  28.146 ms
    # And so on, all the way to:
12  * * * *
13  8.8.8.8  17.921 ms  22678 ms  20.022 ms

Answer 1

Damn, do I feel stupid right now. Like I said in the question, I've added:

network={
    ssid="HomeSweetHome"
    psk=0123464sdasd4d56agr6
    key_mgmt=WPA2-PSK #and so on
}

To the wpa_supplicant.conf file, what I should've done is just add the raw output of wpa_passphrase HomeSweetHome mypasspharse to the file, not bothering with manually adding settings like key_mgmt and others. Everything is working just fine with this:

network={
    ssid="HomeSweetHome"
    # psk="mypassphrase"
    psk=0123464sdasd4d56agr6
}

Thanks for the time, hope this helps somebody else in the future, and please forgive my blind idiocy here...