Windows 7 Can't Update Windows 7 "Low Memory"

So, without a stable internet connection, I have disabled Automatic Windows Update, and have missed out on a couple of the most recent updates (Nearly every single one since 2013). Recently, I tried to download and install all but the optional updates, but ran into a problem. Other than the fact that the update took forever (until I canceled it seeing that I couldn't use my computer during the process) Windows told me that it was low on memory. Everything either completely stopped or slowed to a crawl and it was impossible to do anything. "Just let it sit for a couple of days and it will be fine!" I thought. No. It wasn't fine. It was still stuck on that error saying that I was low on memory! With Windows not responding, I only had one choice. I restarted my computer and tried to restart the update process. The same exact thing happened. I did have an extremely stable connection during that time, but I don't now. Any thoughts?

System Specs:
Windows 7 Home Premium SP1 64-bit
4GB RAM
Intel Core i3 CPU at 2.4GHz
HP G62 Notebook PC