Wifi working but no internet - internet works when wifi is off

Hi - I'm new to the forum and to HTC (just turned on my phone yesterday) so thanks in advance for any help. Sorry for the long description but this should eliminate most questions. Here's my problem - I'll start with the background:

I've been using a basic AT&T phone with no data plan. I ordered the HTC Inspire, and I ordered a data plan. The phone arrived two days ago (Saturday).

My wife opened the box from AT&T yesterday, inserted the new sim card, and charged the phone - without turning it on so that there would be no problems with my existing phone (I was away for weekend). No problems so far.

I returned home yesterday, turned off my old phone, and booted the Inspire with no issues. I walked through the set-up and connected to my home wifi. No issues - I had internet connection. But the phone wouldn't make or receive calls or text messages.

I decided to try my old sim card and that fixed the calling and text problems. I could make calls, and wifi was working.

This morning (Monday) when I awoke I had an AT&T text telling me that they had detected that I was using a smartphone and they were adding a data plan to my account, Although I had already ordered a plan. I figured this was because of using my old sim card from an account with no data plan, so I decided that I would call AT&T over my lunch to straighten it out. Before calling I was able to set up my office wifi - and it worked, I was able to set up my office email, and most importantly, I was able to access the internet while on the office wifi.

I called AT&T at lunch and told them about using the old sim card. They said that my new sim card needed to be activated and I should replace the old sim card. I did this and they activated the phone. I was able to make calls and send texts, wifi was working, and they told me that everything was in order on my account and I was good to go.

I later tried to connect to internet while on the office wifi and it didn't work. I checked all of my settings and it looked good. I'm getting all of my work emails and I'm showing wifi is working, but none of my apps that require internet connectivity are functioning. If I turn off wifi, it switches to mobile and internet works.

Does anyone have a clue what I might be missing? Thank you in advance for your help!

I have some additional info that will hopefully help someone identify my issue:

Last night at home I was able to connect to my home wifi and access data (internet etc), however, my office exchange email gave up. Exchange was working fine earlier at work.

When I left home this morning, data worked fine over the mobile network. At work, exchange email is working again, I'm connected to office wifi with a good signal, but no data (no internet or other services).

I'm hoping this is something simple that I did wrong when I set up my office wifi, but it accepted the password when i set it up and I'm currently showing connected.

So I don't understand why it works fine at home but not at work. I'm tempted to ask the IT dept, however, other smart phone users (iPhone and Blackberry) tell me that they've never had issues so I'm thinking it's something wrong (or complicated and not user friendly) with my phone.