Can I connect two laptops for extra processing power?

I love PC gaming, but my PC is pretty ancient, so I use my laptop. Its decent, but I play everything on absolute minimum graphics, if I can run it at all. Now, my sister just gave me her old laptop that for some reason won't power up right now, and is missing a harddrive. Now, I'm pretty sure I know the reason why it won't power up, so don't get stuck on that detail. Is there some way I can connect these two computers together and make a franken-top to boost my performance in minecraft, even if it is only a little bit. The old laptop I want to salvage has pretty good hardware, a later generation Core2Duo and one of those cheapo intel GPUs.

I connected 4 and accidentally invented the internet

It is certainly possible to connect two laptops and share their resources, however it will only function for software that has been specifically written (or modified) to do so.

The most sensible option would be to repair the highest spec of the two laptops, who may be able to use the HDD and RAM from the older laptop to repair the newer one.

No. It doesn't work that way. It's like trying to connect two slow cars together to make a faster care. You just end up with two slow cars.

Consumer grade software is not written to take advantage of additional processing power like you are describing.