These days, you can get multiple browsers for any computer, tablet, or phone. I have Internet Explorer and Firefox on my desktop computer, and Chrome and Firefox on my Android phone. In addition to these, there's Safari and Opera to make up the "Big Five," plus many other smaller niche browsers. All of these are made in versions for Windows, Mac, iPhone, Android, Linux and more.
For just the sort of situations you encountered, it's always good to have at least two browsers on a device; websites can work on one and not on another, and not necessarily consistently (for instance, you may get a site to work on Safari and not Firefox, while someone else will say the exact opposite). A particular issue I've encountered several times: to log on to a hotel's free WiFi, they gave me codes I had to enter on a website. Internet Explorer was the only browser I could get to work for this login; once online, I could use any browser I wanted (and I prefer Firefox for most things).
If your computer doesn't have the juice to run some of the Big Five browsers, this article on alternate browsers suggests Midori: https://gigaom.com/2014/08/24/six-alternative-web-browsers-you-should-know-about/