This is the simplest and least expensive method to retrieve data off the old drive. Connecting the old drive depends on whether it is IDE or sata, and you should also make sure you ground yourself by touching the case any time you work inside the case. Open the case and insert the drive in a vacant drive bay.
If the drive is IDE, make sure the jumpers on the old drive are set to cable select and attach the ribbon from the old drive to the secondary drive connection. Connect the drive to the power supply using an unused power plug. (if one is not available get a Y connector from the computer store for a couple of dollars). Boot up and the OS should recognize the new drive. See if you can navigate to the files you need to transfer. Hopefully the blue screen problem was caused by the OS and the drive is still functional.
For a sata drive, connect the drive to the sata connection using a sata cable. You also have to connect the drive to the power supply, and the plugs are different than the ones for IDE drives. You also might have to enable the sata drive in the BIOS. Boot up and navigate to the files.
If the drive is working OK, you can reformat it after you retrieve all the files you need and use it as additional storage.