it doesn't matter where we put the game with such a slow connection. And even if we fix that part, it'll probably be unplayable.

Well here's what I understand about the patching process: You have the majority of the game downloaded already, and the patch updates simply download any new data that OOO may have updated or changed, and therefore replace the older versions. I cannot say for certain if uploading an instance of a SK root folder would actually work, I get the feeling it is a bit more complex than that, but I would need to hear from someone who knows before uploading the entire game.

One other note - Java isn't the problem. I also don't know if your connection could possibly be blocked given your country of origin.

It won't work.
If it did work with your father's PC, shows this game was on it before.
So basically, (this is how I THINK it is, not sure...)
This game is composed of several data files, and a root file, which is the game programming itself.
However:
1. Copy pasting the SK icon will do absolutely nothing. That only copies the icon used to transfer Internet data into the java program, which utilizes the Internet data it receives as well as the data files originally downloaded to play spiral knights. If you were to just copy the SK icon, it would say something like "missing files :xxxxxxxxxx-:xxxxxxxxxx" and you won't be able to play.
2. If you meant for someone to copy paste the entire game to you, I'm not sure, but that may be against OOO terms and agreements, of which to not distribute the game in certain ways... Not sure, as you technically aren't editing their base programming, but...
3. If you mean to copy the SK launch app, then once you open onto the computer, it would still need to download, because just the app for SK is not enough. You also need the base data, the root files, the online data... You would still need to download those. And based on your information, I think either something happened to your Internet while you were downloading, or your computer somehow ran out of memory, but it has nothing to do with SK itself. It has to do with downloading the files that are needed to OPEN SK.

Not sure if this is true, this is how I think of it... Hope I helped
~Apop

It's against the ToS to redistribute Spiral Knights.

You're missing the point, I believe.

It is against the Terms of Service to, and I quote, reproduce, distribute, publicly display or perform, translate, modify, adapt, create derivative works from, deconstruct, reverse engineer, decompile or disassemble in any manner Spiral Knights or any portion thereof, including but not limited to any character, graphic, associated software or proprietary communications protocol used by the software or any utilities, applications, emulators or tools derived therefrom;

The actions you intend to take with an illegitimately acquired copy are irrelevant here, it is the the process by which you intend to acquire the game that violates the Terms of Service.