If your old computer no longer works because of the lightening storm then you will have to remove the Hard Drive from the computer and connect it to your new computer.
You can connect it to your new computer via the USB port, just like any other USB device.
You will need an IDE/Sata to USB Adapter plus a power cable. Its not that expensive. Search on ebay.
Once you connect it to your new computer via USB, goto 'My computer' and you will see the new device there. Double click it and search for your Documents/Pics etc, then copy and paste them to your new computer.
Hope this helps.