uBlox LEA 6H and UNO no data
Your uBlox LEA 6H is most likly configured to use the UBX binary protocol and not NMEA at all. This protocol, as well as how to switch your LEA 6H between NMEA and UBX is in this document, from the uBlox website:
http://www.u-blox.com/images/downloads/Product_Docs/u-blox6_ReceiverDescriptionProtocolSpec_%28GPS.G6-SW-10018%29.pdf

You may be able to use the code from the ArduPilotMega project to communicate in UBX, they use the UBX protocol and the code is open source, but I can't guarantee its very good quality.