Verification of problem in arduino uno

Sir,
I recently bought an Arduino Uno R3. When I connect my arduino through usb cable, the pin no. 13 led goes high by default, that is it ON consistently.Is it normal, or there is a problem with the board? I have tried uploading an empty sketch, but with no results. It keeps glowing. I uploaded a sketch declaring pin 13 as an OUTPUT pin, only then it goes to OFF conndition. But when I again upload an empty sketch, it goes ON again. Also when I measured the voltage in the Rx and Tx pins of the board, the Multimeter read 4.8 and 0.2 respctvly, though nothing is being uploaded and the board is sitting idle. Is it normal or the board is faulty? A quick help will be appreciated very much.Thanks in advance.

Usually the Uno comes pre-loaded with the blink sketch. The first time that you hooked it up, did pin 13 blink?
If not, it was either not loaded or somebody returned it and next the dealer sold it to you; if you bought it from the internet (amazon, ...) that might be a real possibility.

The fact that TX only reads 0.2V is worrying. I would double check that as it would be strange that an upload would work if the the TX pin is damaged. I verified it and both TX and RX are close to 5V on my board.

When you load the blank sketch, the LED will be on with an original Uno (I've just verified it). I also have a Sparkfun Redboard (clone) where the LED is off when using a blank sketch; this is due to a difference in design of the two boards.