Yeah, it didn't work on any browser. The error that I got was "Error launching Unity" or something. I read that some people had previously gotten an error that was identical to mine apart from theirs being along the lines of "Error launching Unity dll".
Fortunately, it fixed itself when I restarted the computer. I'm pretty confident about computer use, so I can't believe I didn't think of trying that sooner. Still, I'm surprised that uninstalling then re-installing unity from scratch didn't fix anything, considering that *should* be programmed to wipe everything unity related (which it doesn't, there's still plenty of local files remaining related to unity after un-installing).
Unity seems to have a host of problems atm, from what I read yesterday. Some are related purely towards Chrome while some are related to older computer hardware (Unity appearantly stopped supporting some old versions of hardware still much in use with no warning or notes). Then there's the seemingly random ones like what I had.
Again, it fixed itself. Note to anyone having this problem - Try restarting your computer. If that doesn't work, un-install then re-install Unity and restart your computer.