afterAfter dealing with the problem for several hours I unexpectedly solve the problem.
The HC-06's LED keep blinking after I entered the "1234" code. Looks now to me that this is normal. In my case (I'm using Windows 10), the HC-06 status changed to "connected" for few seconds and then changed to "Paired". Once I opened the correct COM port to receive data from the HC-06 to my PC computer, the LED changed to solid ON :). Then I was able to catch data from my Arduino UNO. As soon as I closed the COM port in my PeCePC (I used CoolTerm), the LED changed to blinking back again. The COM port I used to receive the data was the one indicated with direction "Outgoing" in the PeCe'sPC's Bluetooth settings. So, I was expecting the HC-06 to behave as my Bluetooth speakers or my Bluetooth headphones: Always connected. I was wrong and it cost me several hours of testing.
In my firsts testtests I focused opening the COM port with direction "Incoming". Nothing happened here and I lost a lot of time. I tested my wiring between the arduino and the HT-06 module by changing the device name from "HC-06" to "ArduinoBT01" and it worked.
This is the sketch I used to receive data form the Arduino via Bluetooth:
This is the CoolTerm's window capture:
Mysteriously, the CoolTerm speed setting is 14400bps but the speed in the device manager for COM34 is 9600bps. After triying opening many times the COM34 port with 9600bps I got this error in CoolTerm:
"An error Ocurredoccurred while attempting to open the port". "1168: Error 1168"
So, it only works with 14400 bps. Crazy!!
I hope this helps.
Sorry for bugs in my English.

