My wife got a device upgrade this August, so I've recently had the unfortunate pleasure of being downgraded from my unlimited data to the "Share Everything plan." Since then, 08/18/2013 I have not been able to get 4G LTE, 3g, or even a 1x data connection on my device. My wife is also having the same issue with her galaxy s4. The plan change is the only change I've made to my account, I haven't changed any device settings.
I've used chat twice, they "put in a ticket" to see if they could identify the issue. I got the "you're located in a marginal coverage" area response, so apparently the state of colorado is a marginal coverage area because it happens everywhere.
I went into a Verizon store, had a helpful agent suggest that maybe I needed one of the new NFC sim cards, that worked for all of 30 minutes now back to no connectivity.
I've attached a screenshot of what I've noticed. Normally during an "active" data session the 4G icon and signal bars will turn blue. this doesn't happen anymore.