Here are the specific steps I've taken so far to make sure it is not a problem with the phone itself or some other obvious issue with settings. Of course, I called customer service each time using a different phone from the one experiencing the problem:
--Called Samsung customer service, did a factory data reset on the proclaim, made sure WiFi was turned off (so it wouldn't be searching for a WiFi network), and made sure that under "Mobile network settings", the "Use packet data" option was checked. At that point, the Samsung rep said it sounded like a service problem.
--Called Straight Talk customer service. Steps similar to above, except the rep "checked" my phone and service from her end. She asked me to make a call - I did since I've have had 3 to 5 bars of service all along - and she assumed the issue was fixed. I explained that the phone was fine making calls, but wouldn't make a mobile network connection ("No network connection. Cannot connect to the Internet. Please check your connection settings and try again.") I asked her specifically if "Data roaming" needed to be checked off; she said no. Back to the "call *22890" instruction, received that voice message that programming was complete, but browser still didn't work. Service rep said to wait 15 minutes and then turn the phone off and on again and ended the service call. Needless to say, the problem was not resolved.