It appears that the charset of your connection is not set right, therefore the conversion from the programming language charset to the database is not correct.
You should set the charset in your connection, then both will workfine.
as pointed out in the comments a little explanation on how things work.
when you have not set the character set in your connections, the server assumes it to be the same as the collocation of the database. when data is recieved in a another encoding, the data is written nevertheless. just with wrong or other characters than they have been in the encoding of the data from the script.
as long as nothing changes, the script gets back the same data as it has written and everything appears to be fine.
however when either the connection encoding or the database encoding is changed at this point, the already stored data gets converted to the new encoding. the problem here is that the source data is not in the encoding that is assumend when converting.
all encodings share the ascii set with the same bits, thats why ascii charactes dont mess up. only special charaters do.
so you have to set your conneciton encoding in order to dont produce the mess that you are already in.
now what can you do about the data you already have?
you can make a dump of your database using mysqldump and use the --skip-set-charset
option. then you get a plaintext file. in this plane text file replace all occurences of the actual database charset with the one the data is really in (the one you had in your script when you wrote the data).
then save the file and make sure your editor does not do any conversion (i recommend vim).
then import that file and you will get a database with data in the correct encoding. then you can change the encoding however you like and as long as your conneciton charset gets set also you will be fine from now on.
also make sure that the mysql server has the charsets installed, but it should have that already.
this is only my approach, i have cleaned up a lot of messed up installations like that. most of which at some point have garbled characters in their projects (after switching server, updating or restoring a backup...).
turns out not setting the connection charset is something that is very often forgotten.