Success! Wow! I backed up the files on my internal memory card to my replaceable one, then formatted the internal memory. I am now able to install Skype (haven't tried anything else yet), and it works!
I am indebeted to all who helped here. I'll buy the next round of adult beverages of your choices (or dinner, or whatever). I do appreciate the help very very much!
Now the magic question - well, two of them actually. Why was it that a brand new N810 had this problem - I wonder how many other unsuspecting buyers there may be out there. Secondly how did you all get this experienced with diagnosing and fixing such problems?
Above all, thanks a lot.