if the compaq laptop has a VGA out, it should mine has and if the 32inch Phillips LCD flat screen tv has a VGA connecter on the rear.
Then yes. Just get a VGA extention lead. Connect the cable to the laptop and then to the TV. Switch the TV on to the AV channel or scan the AV channels ( my philips 32" has 4 ).
The desktop screen will appear.
Right click the laptops desktop and pick properties > settings > pick TV screen number 2. Alter the sliding settings to get the best result.
A compaq / HP laptop running media centre on a 55" TFT at a resolution of 1920 X 1080 click here