How? He used that computer to buy stuff online

The internet is not the only place to buy things. It's also not strictly necessary to buy a computer solely to access the internet. For instance, you could ask your neighbour if you could use theirs for an hour or two or go use one at the local library. Especially if it's just to book a, what seems to be, very important trip while you're dying of cancer.

EDIT: Grammar

He clearly told his son about it.

And it's take not much more effort to order a laptop than to comment about it on HN.

To quote the parent post, "He was too tired to go through the process of getting it sorted out".

I don't know if you've ever been really sick (or just been around someone who's really sick or suffering from chronic pain), but being on chemo is a thing that completely shuts you down. I fully believe that going out to the store and buying a new laptop and getting it set up was beyond what the parent-poster's father felt capable of. Similarly, going out to the library and doing it all from a shared computer would be entirely too much. Anything that's not the well-worn familiar path would feel insurmountable.

I get this. I mean his son.

I bought my dad a laptop this summer and he's quite healthy.

I just assumed some sort of not-living-in-the-same-area situation.

My father was indeed too tired to do anything much in the immediate aftermath of chemo. I would cheerfully have booked and paid for the holiday myself, but he didn't tell me about it at the time. He wasn't much one for asking for help.