Such an old computer is too old for connecting to the Internet using any of the recent browsers and as you have found out the older browsers are too outdated to access the Internet of today. Years ago some people did try to backport & maintain some web browsers such as Firefox to keep these older systems online, but most of those people have moved on & their projects abandoned since it is no easy task.
How do you wish to utilize this 15+ year old Mac? If you have old apps you wish to use, then do so as long as they don't need an online component.
If you only want to use this old Mac for browsing the Internet and basic tasks like word processing or basic photo editing/management and the Mac is a 2007+ Intel Mac, then you may want to consider installing Linux Mint on it. If the computer has at least 4GB of memory, it will work well with Linux Mint, but if it has only 2-3GB of memory, then only very basic tasks can be performed such as only one, maybe two browser windows/tabs open.
Before even considering this, you should first make a bootable macOS USB installer if your Mac is able to run macOS 10.11 El Capitan (and test that it can boot that installer). You would need to use another current computer (macOS or Windows) to download the DMG installer & transfer it to the 15year old Mac where you extract it & create the USB installer.
Create a bootable installer for macOS - Apple Support
You can even test drive Linux Mint by booting the Linux Mint USB installer and selecting the "Live" option where it will run from the USB stick.....performance will be extremely slow, but should be acceptable once installed to the internal drive (assuming the internal Hard Drive is even healthy). At least it will you an idea of what to expect. Many of the popular web browsers can be installed (Firefox, Vivaldi, Brave, Google Chrome).
Linux is not for everyone and it does require learning a new OS, but it is a great way to extend the useful life of an old Intel Mac......only from 2007+. Some 2006 Intel Macs should not have Linux installed since it could brick them (especially the 2006 white MacBook with 32bit only Core Duo CPU....personal experience....twice)
