Learn English – Politics: singular or plural

According to Oxford Dictionaries it can be "treated as singular or plural".

Personally, I find the plural form more natural in your example. Also note that you need another "to": There are no means to listen to what he is saying.

Part is not actually correct here: it would be most of the banks. Since most (the subject) is plural, you should use the plural copula are:

Most of the banks are corrupt.

However, if you reword to bring part back into the sentence (e.g. A large part of the banks), then part becomes the subject, hence you would use the singular copula is:

A large part of the banks is corrupt.

Since it sounds strange for is to come right after a plural noun (no matter how grammatical it is), we usually steer clear of such sentences. In fact, since the words "a large part of the banks" actually refers to a plurality, it would be completely fine to use are as the copula:

A large part of the banks are corrupt.

However, if you want to avoid pedantry from whichever side of the debate you don't choose, you may decide to simply use most of the banks are corrupt.