Hi Mike
Assuming your hard drive is still in working order and uncorrupted by the lightning strike I don`t think it should be too difficult.
I had a similar problem and got round it by buying a :- USB 2.0 to SATA IDE Hard Drive Adapter Converter Cable, of Ebay in the UK for approx £7.USB-SATA-IDE-Hard-Drive-Adapter-Converter (brilliant piece of kit and worth every penny)
Just remove the HD from the old computer and power it up on your desk using the purchased device and connect to your new computer USB port.
Open Windows Explorer on your new computer to view the contents of your old HD and "Drag and Drop" or "Copy & Paste" the files required to your new computer.
If your old HD is corrupt as mine was you may require some suitable software. I used "EaseUS Data Recovery Wizard" (not the free edition) although the free edition may be worth trying before going to any great expense.
Hopefully your HD is uncorrupted.
Hope you fully understood my explanation and good luck.
Regards
Danny

 

We have great success installing the old or suspect drive in a USB external enclosure... which you can purchase for $7.00 to $35 in the USA, depending on quality and size... but you need one with its own power adapter to run a suspect drive successfully...

Then, since you already know what is on the drive, you can plug the external drive into your USB slot... the working computer will identify the external drive by giving it a letter, then drag and drop all the files, a few at a time... onto folders you have already named in the new system.
Do NOT turn off the external drive until done, for best results... because you don't know how much longer the old external drive will last...
then burn to a DVD all the files and photos you have copied over. Inspect them to assure they are good and working files.
Now you can do whatever you want with that old drive, but your files are safe... as you nnow have a copy on a hard drive, and have burned copies to DVD's.

 

Mike
Not sure where you are located but the piece of kit I told you about is sold by Amazon in the USA and described as :-
SATA/PATA/IDE Drive to USB 2.0 Adapter Converter Cable for 2.5 / 3.5 Inch Hard Drive / Optical Drive with External AC Power Adapter (sorry not sure how to add a link)
The price is $8.90
It comes complete with everything you will need including the AC power supply raybay commented on. It does not include an external enclosure.
My hard drive was from a laptop with no exposed components and did not require an enclosure. If it is a 3.5" hard drive with exposed components you would need to take care that nothing came in contact with them or purchase a enclosure as raybay suggested.
Regards
Danny