That is a too old of a laptop. In reality, modern Linux distros run well in anything newer than 10-15 years. Yes, there are distros that you can install into it, but they won’t be the latest and greatest distros of today. They’d be instead distros made specifically for old computers, and these distros are usually more complex because they lack all the gui tools found on newer distros.
First you need to find out if your CPU is 32bit or 64 bit, and if it can take a minimum of 2 GB of RAM (if yes, upgrade it too). Then, I’d suggest you download the right file from here: https://www.q4os.org/downloads1.html I find Q4OS to be the best for old computers (more gui tools), but you’d need that minimum of 2 GB of ram to load a browser and be comfortable with 3-5 tabs (no more than that though or you’ll hit the swap). Also, consider Falkon or Chromium as a browser, they use less ram than firefox (people have downvoted me for saying that in the past, but it’s my experience).
Personally, I’d get a used laptop for $150 from the last 10 years, and install Linux on that. It should be way faster than your Asus laptop. Just make sure it has 8 GB of RAM to be comfortable with modern Linux distros (Linux Mint can work adequately with 4 GB of RAM, unless you want to do video editing).
If this happens to Windows as well, it’s unlikely that it’s Fedora’s fault. Something else is at play.