I ran into a similar issue when trying to get composer to install some dependencies. It turns out the .dll my version of Wamp came with had a conflict, I am guessing, with 64 bit Windows.
This url has fixed curl dlls: http://www.anindya.com/php-5-4-3-and-php-5-3-13-x64-64-bit-for-windows/
Scroll down to the section that says: Fixed Curl Extensions.
I downloaded "php_curl-5.4.3-VC9-x64.zip". I just overwrote the dll inside the wamp/bin/php/php5.4.3/ext directory with the dll that was in the zip file and composer worked again.
I am running 64 bit Windows 8.
Hope this helps.