Device unable to be found - Error 1119 (System Software Updates)

I am using an iPhone 4, attempting to update from iOS 7.1 to iOS 8+. System Update utilities in both iTunes on my computer (an Acer Aspire running Win7) and on my iPhone have not been able to detect or download iOS 8+ for installation and only provide iOS 7.1.2 (not what I need). Additionally, I have received error messages when trying to update from both my computer (Error 1119) and my iPhone (which just says that there is an unspecified error).

I thought it could be caused by faulty USB ports on my laptop, but the problem occurs even when updating over WiFi, so I'm at a loss to what causes it. I've tried restarting my iPhone and computer and almost everything short of restoring my iPhone from a backup (to hopefully restore software update recognition) and/or reinstalling iTunes.