What apps have you installed that might affect the display timeout? Something's keeping the display from turning off.

Also, if your phone's display actually stayed on as you you say, the Display should be the highest percentage, not Cell Standby.

Finally, how many hours of battery do you have? I get about 13 hours of battery life and I surf on it constantly or play games on it once I get home from work. 13 hours is great...as I came from a WinMo phone that only held a 6 hr charge.

If you came from a dumbphone, you have to let go the expectation to only charge your phone only once every 5 days (that's what I could do with my Nokia flip phone).

Smartphones need to be charged at night, every night. You can't avoid it.