Hi,
You must take more care as this is quite simple code that we are working with but you are missing some simple basic things.
First of all you have changed your code back to classes but you have only changed one of the classes in the css. You still have an id here and a space after the span
span.left_quote, [B]span #right_quote [/B]{
text-indent: -999em;
width: 57px;
height: 57px;
background: url('http://www.muslimahwebdesign.co.uk/wp-content/uploads/2013/05/left_quote_turn.jpg') no-repeat 0 0;
padding:0;
}
It should be:
span.left_quote, span.right_quote {etc...}
A comma separated list as above (span.left_quote, span.right_quote ) is useful for shortening the stylesheet as you can apply common rules to a group of selectors in one go.
If you say:
.test1,.test2{color:red;background:white}
It’s the same as saying:
.test1{color:red;background:white}
.test2{color:red;background:white}
Except that it uses far less code.
You also have another error here where you have an extra closing bracket:
.quote_top {
text-align: center;
margin: 0 0 1em;
}
[B]}[/B]
.quote_top span {
display:inline-block;
vertical-align:bottom;
padding:0 5px;
}
That extra bracket will make the next rule fail as it becomes part of the selector for the next rule.
Here is your code once again in working order (as it has been every time I have given it to you) 
.quote_top {
text-align: center;
margin: 0 0 1em;
}
.quote_top span {
display:inline-block;
vertical-align:bottom;
padding:0 5px;
}
span.left_quote, span.right_quote {
text-indent: -999em;
width: 57px;
height: 57px;
background: url('http://www.muslimahwebdesign.co.uk/wp-content/uploads/2013/05/left_quote_turn.jpg') no-repeat 0 0;
padding:0;
}
span.right_quote { background:url(http://www.muslimahwebdesign.co.uk/wp-content/uploads/2013/05/right_quote_turn.png) no-repeat 0 0 }
I also note that you have included style tags in your external css file which is not allowed and will break the rules.
[B]</style>
[/B].styled-list #top_list li { list-style-image: url(http://www.muslimahwebdesign.co.uk/wp-content/uploads/2013/05/arrows_2sm.png); }
Remove any style tags from your external css.