Hello Shahab,
Thank you for replying to provide some additional details.
It sounds like your 19'' display is working normally with your older 15'' MacBook Pro, but doesn't respond at all when connected to your new 13'' MacBook Pro.
Based on this, I'd recommend trying these specific steps from Troubleshooting issues with video on internal or external displays on your new MacBook Pro, testing your display in between each step:
Reset the system
You can reset the Mac's parameter RAM and SMC.
Reset the resolution
- Start up in Safe Mode.
- From the Apple () menu, choose System Preferences.
- Choose Displays from the View menu to open the preferences pane.
- Select any resolution and refresh rate that your display supports.
- Restart your computer.
At this point, if the display still doesn't receive a signal, try testing your 13" MacBook Pro with another Thunderbolt adapter or display, if possible. This will help to further isolate the issue to the display, adapter, or MacBook Pro.
You can also seek more help from an Apple Store or Apple Authorized Service Provider:
If you tried all of these steps for your display and the video issues persist, contact Apple technical support or take your Apple computer to the nearest Apple Store or Apple Authorized Service Provider (AASP) for diagnosis. If you plan to visit an Apple Retail Store, make a reservation at the Genius Bar using http://www.apple.com/retail/geniusbar/ (available in some countries only).
All the best,
Jeremy