Transferring to different server, same url

I am trying to transfer my friend’s WordPress blog to his new server. The URL is the same. I got everything transferred, and I’m 99% sure I did it right. I followed all the instructions on the WordPress codex, and it appeared to be working, all the posts were there, the blog was there, but I discovered that if I tried to click a link to see a certain category of posts or to go to the about page, I would get a 404. If I pointed the nameservers back to the old server, it would work again. The files and file structure on the new and old server are exactly the same.

The reason we are moving to a different server is because on his old server when we installed a different WordPress site (there was already one there, and we added a second), they would both randomly start going down with 404 errors, just the WordPress sites, at the same time, but everything else on the server would work. I’m sort of a novice at this, so I had a friend of mine who is a web developer look at it, and he just told me that he needed to switch to more professional hosting because of something about htaccess files.

I was trying to just get it to work locally with MAMP, but I kept getting errors about not being able to connect to localhost.

I have been working on this for days, I’ve been Googling and searching the forums, and I can’t find any solutions. I’m so frustrated. Does anyone have any suggestions? I’ll take anything anyone can throw at me at this point.