It's very hard for us to say whether it's hardware or software, since all we know is the bottom of the digitiser doesn't work. If the phone is unrooted and has never been rooted, so no modifications have been made to the system software, my feeling is that it's unlikely to be software. You might want to ask your cousin whether she/he's every fiddled in that way, but even if they have it would be a very odd bug, and an odd thing to just suddenly happen. I assume you've done all the usual stuff like pulling the battery out for a couple of minutes, just in case that clears something?
If you want to be sure you could back everything up and do a factory reset, which will wipe all apps and data apart from pre-installed stuff. That would rule out the possibility of a user-installed app causing the problem, and if the system software has not been modified you could be fairly sure it's hardware. I'd certainly try this before I took it to be repaired.
To be honest though I think hardware is more likely. You may never have dropped or damaged it, but how well do you know the phone's history? If it had had some drops in the past it might be that something was loosened or damaged and has just now broken or come out. Or if it had got wet at some point in the past corrosion might just now have caught up with it (even if she/he thought they'd dried it out). Or something might just have failed without any mistreatment, as sometimes happens.
As to whether it's repairable, that depends on the nature of the problem. If it's a loose connection, easily repairable. If the digitiser has simply failed, yes, but will cost more. If it's the result of historical moisture damage there may be other damage as well. The bottom line is that I doubt you'll know how repairable until the phone is opened up.