Sounds like a hardware problem. DEMAND FOR A REPLACEMENT!

When I bought my second N4, I had a similar problem. It would connect to 2G but never 3G. LG replaced the whole unit for me
Current Devices :
LG Nexus 5
LG Nexus 4
Samsung Galaxy Nexus
Sony W810


Ex Devices :
HTC Dream - SOLD
HTC HD2 - Water Damaged :'(
LG Nexus 4 - Stolen </3
HTC Sensation - Retired
Nexus One - Retired
ZTE V9 - Retired


My Google Plus
My Website
Transparent StatusBar Mod Thanks to ZduneX25
Register for Dropbox here