|If the hard drive is still working then you should be able to access the data on it.|
The method to use depends on what type of interface the laptop drive is and what type of connections you have availible on your new computer.
One sure and easy method is to get a special USB adapter that you can connect to the laptop drive and to a USB most on most any PC. Examples of those cable connections can be found at the link below.
The most useful units are the ones that will connect to all the following: 2.5" & 3.5" IDE/ATA and SATA hard drives.