Hi I have been having trouble with the 1.7.10 forge not letting me use any of the 1.7.10 mods i have tried multiple versions of it but it never works no matter which version I use even the recommended and latest.
If any of it doesn't make sense just let me know and I'll try to simplify it more. Otherwise try using a Youtube tutorial if that works better than text and how I presented my comment. And sorry if it's a bit long, just wanted to make sure I got everything needed in the comment.
1.Did you start the game with the Forge 1.7.10 profile [refer to image 1] (that you would have installed of course) and have no mods in the mods folder to see if it works.
You need it before installing Forge as Minecraft's built can't.
I assume you don't know the difference between 32bit and 64bit, but this is important.
If you can find a way to see if you have a 32bit computer or a 64bit one that will help.
The easiest way to do this is to (at least from what I know with Windows 10) is you can go to the search bar on the taskbar and search 'system information' once you have done that a window should come up not an Internet search. (Refer to Image 2, the 64 PC one and Image 3 the RAM one).
If it says 64 then either 32 (I recommend the offline) or 64 is fine. 32 can only use 32 though. And the RAM is another way of telling, if you have more than 3GB of RAM then you know you have a 64bit PC as 32bit ones can't use more than 3GB of RAM.
By getting Forge or mods from other sources they can be fakes/have viruses in them. That's why it's best to get from the official or safe sites.
2.Did you get mods from Curseforge? Like the point above about fakes/have viruses inside the files, Curseforge is a safe content hosting site, ones like 9Minecraft are repost sites and steal files from the creators. There is 1000s out there, if you want to check for the site you used to see if it's a repost site and how bad it may be you can compare here: https://stopmodreposts.org/sites.html
3.If you have crashes it's good to look for a crash report so someone that understands them can read it and find out the problem.
You can find crash reports in the same space as where you add mods to the mods folder (in your .minecraft if you know where that is after seeing a tutorial, the easiest way to get to .minecraft is to go through the resource packs menu under options and you will find the resource packs folder from the left button in that menu, back out of the resource packs folder and your at .minecraft.
If Forge didn't create a mods folder for you as it's supposed to just create a new folder and call it 'mods' with no capitals and put your 1.7.10 mods in that folder).
If you don't see a crash report just move mods out of the mods folder. I also do this (even if tedious and boring) but it helps me to know which mods is causing problems for me.
If you want things to be easier than that just try using Modpack Launchers like Twitch or Technic and it will make auto mod downloading, setting up Forge and installing modpacks quicker and easier to understand than the Regular launcher way where you have to know where the folders are and look around the Internet more and can stumble across viruses.
Hopefully that helps. If it was too confusing let me know. It took me a bit at first when I got into modding back and got Minecraft Java in 2012/1.4.5, now it's easy after doing it so many times and for so many years.