my $query = "UPDATE staff SET password=$FORM{'newpassword'} WHERE $FORM={'name'} eq $ +record{'login'}";

Are you really sure you want "WHERE $FORM={'name'}" in your query? You use $FORM as a hash, and then use it in scalar context - so your query would get passed to your DB as: "... WHERE HASH(0x013221)={'name'}", or some other garbled mess.

I think you probably want "... WHERE name=$record{'login'}", or, making things simpler (and safer), using placeholders (if your dbh supports it) such as '... WHERE name=?'

Update: just one other quick thought - if your input is coming from a CGI form, as your $FORM variable indicates, you should be using the CGI.pm module. It'll save you a lot of headaches. :)

Update (again): just looking things over now, $FORM wouldn't print HASH(blahblah) - it wouldn't print anything. Once again, I'd forgotten that you can have $FORM and @FORM and %FORM and sub FORM{}, all at the same time. 'use strict' is good for finding your type of error, btw.