I downloaded Morrowind Sounds and Graphics overhaul and after I installed it, it took me to the code patch screen where I could check and uncheck things I wanted to get patched. When I was all done with that I clicked "Apply chosen patches", but it gave me this message:

anolyzing Morrowind.exe...
Backing up Morrowind.exe to Morrowind.Original.exe
There is no compatible patch for your version of Morrowind.exe. Make sure your Morrowind is patched with the last Bloodmoon patch (v.1.6.0.1820). If you should have a compatible version, please check you have not installed other patches such as Exe Optimizer, fpu2sse or no-CD patches. Check the readme for more details.
Patch failed to apply.

Does anyone know how I can fix this? I've patched it to the latest Bloodmoon version, but it still won't work! And when I click "Uninstall all" to get out of that menu, it says:

Restoring from backup..
Could not find a backup of Morrowind.exe.

Uninstall failed.

So I'm pretty much stuck at this menu! Can someone help?

What version of the game do you have? What does it say at the bottom left hand corner of the main menu if you start up a game before applying the Morrowind Code Patch? From the look of the error message you received you need to apply the latest official patch before using the MCP. I don't think the MCP will have modified your Morrowind.exe if it didn't find the correct version, but if it did you should be able to replace the Morrowind.exe file with the one found on the retail disk, then apply the official patch, then finally reapply the MCP

The official patches can be found here: http://www.gamesas.com/downloads_01.html

1) You have to start with a fully patched Morrowind.exe. That means either a GOTY edition, or a Bloodmoon patched up (link above).
2) You cannot have run any other modifying app against the exe first. These include Exe Optimizer, 4gb patch, various nocd patches (that don't usually work anyway).

You need to start with a completely clean exe. For some reason it will apply to exes that have been modified by MCP and all the other types of changers later on, but it won't apply the first time unless the exe is pristine. Make a copy called "Morrowind_Original.exe" and keep it forever in your game directory so you don't have to re-install all the time. MCP makes a copy, but I find it better to make my own that I can guarantee is the original game install.