Try running
sudo rfkill unblock all
Then configure the wpa settings just like you did, save, then reboot.
iwconfig will show you if the wifi is connected or not
NOTE: if you don't have any spaces in your wifi ssid or psk, you don't need the quotes.
Here's some additional config options for /etc/network/interfaces
For dhcp
auto wlan0
iface wlan0 inet dhcp
wpa-ssid blahblahname
wpa-psk blahblahkey
For static
auto wlan0
iface wlan0 inet static
wpa-ssid blahblahname
wpa-psk blahblahkey
address 192.168.1.234
netmask 255.255.255.0
gateway 192.168.1.1
dns-nameservers 192.168.1.1 8.8.8.8 8.8.4.4
dns-domain yourdomain.com