Patching issues on a fresh install Error 004

Hi, I'm having problems patching League on a fresh install. Small backstory; I played on this laptop a few months ago, then uninstalled, now I want to come back. I bring this up because League was working, at one point, on this machine.

1. My download speed will fluctuate wildly between 300kbps and 1300 kbps. This isn't really a problem as much as it is an irritation, since I'm happy as long as it's downloading. Any advice would be great regardless.

2. When I reach ~70% download, Error 004 pops up and tells me to restart the client. I've been doing this for probably the past 6 hours, and nothing I've tried so far has seemed to help.

I've attempted Admin rights and Hextech Repair tool. Interestingly, the Hextech Repair Tool actually crashes every time I try to use it so that may have actually just been wasted time.

The most frustrating part about this is that I'm wasting about 2 hours of download time every time I have to start the process over. Why does Error 004 (which from what I've been reading is either a network or permissions error) clear all the progress I've made until that point and start from square one? Are there any mirrors or anything I can do to make the process iterational instead of the all-or-nothing I've got going now? 2 hours to fail constantly is definitely not making me want to play again.

Any other help on fixing Error 004 would be much appreciated!