Unfortunately, I would say you probably have a hardware issue here. I have had two phones do similar things, one did not connect at all, the other would connect only for a moment before basically shutting the GPS down. Both of these ended up being hardware issues resulting in me returning the devices. My best advice would be to try multiple apps to test GPS signal, ( I use GPS Status or Tricorder), and if you get no GPS reception from any of them, contact your manufacturer, or the people you purchased it from. Usually resellers will refund or replace products that malfunction without provocation.
If you do get signal with any of them or you get partial GPS signal sometimes, I'd still contact your reseller or manufacturer with the issues, while continuing to test it in different places alongside other (Android 4.0, if possible) devices.