I don't know why B&N would tell you that Twitter is not an option for the NGL. Now, while you can't have a fully functional app with feeds and updates like on your phone, you CAN connect it to Twitter to post quotes and such from the NGL. The option is in the Social tab under your settings menu. Maybe I'm misunderstanding what they said.
I have my NGL connected to my Twitter and post from it all the time. So, their comment is baffling.
The blank screen might just be a bug. You can take it into the store and see what they can do, maybe even replace it if you have a warranty. Or, check the settings on your twitter account and see if you don't have some privacy permissions conflicting with the setup.
I don't really have any advice though since I've never encountered this bug. I just want to let people know the NGL does have Twitter connectivity capabilities.
I suspect the support person thought you wanted to put twitter on your NGL. I don't know why they would assume that since it's one of the things I've trained new booksellers about, i.e. that the eink Nooks don't allow social networking apps, but you can link to them for sharing things.
The only thing I can think of without having physical access to the NGL is that there's an issue connecting it to Twitter. Which can have a few causes, Twitter servers being glitchy (unlikely, but it can happen), the NGL being in low/weak wifi, or not actually being connected properly to wifi.
A quick test to see if it's in wifi is to open the shop, if it loads you're in wifi, if it doesn't you're not. This is a better option than looking at the upper right hand corner since that indicator can be a false positive, i.e. it claims you're connected but you in reality do not have internet access.
I haven't seen this issue in my store, nor on my NST, NSTG, or NGL when I used to have them linked. I unlinked them because my friends have very different tastes in books and it was giving me suggestions for things I would never read.