No you are not being paranoid.
I have become well versed over the last few years with faulty tvs as i've been on the receiving end of my fair share of them (lcd and plasma) and in my opinion your tv is faulty, either one of those issues seems bad enough to reject the tv on it's own but the combination of the two is simply not acceptable.
Richer Sounds was where i purchased my GT30 plasma and despite having issues with 2 of the tvs i received they couldn't have been any better and replaced the tv on both occasions until i received a set i was happy with so i'm absolutely sure they will look after you so you shouldn't worry just take it back and they will look at it and not fob you off from my experience, they are the best retailer i have come across. If you look at the back panel of your receipt you will see that if you get a fault with the tv in the first 30days you have the right to return it for a replacement or full refund and it's not a painful process i can assure you,
If it was me i would just return the tv to the store despite it being a pain as i think you will get a satisfactory resolution, just be glad you bought from Richers as alot of retailers seem to require you to battle them in order to get the tv replaced...i speak from bitter experience. I won't buy from anywhere else now after the excellent customer service i received.