Here's a rule of thumb. You do not have access to the clients file system.. When you execute this:
$fp_remote = fopen(htmlspecialchars("c:\\image\\").urlencode($home_picture), "rb");
PHP is attempting to open a file on the local file system which in your case looks like a linux file system.
You can only look at files on a client mchine using FTP, which would require the client to have an FTP sever running on their PC. You can however ask a client to submit you a file. You can do this with a simple HTML form:
<form action="file-upload.php" method="post" enctype="multipart/form-data">
Send these files:<br>
<input name="userfile" type="file"><br>
<input type="submit" value="Send file">
</form>
When the user presses the submit button the file is copied from their computer to your computer. You can then get at this file using the move_uploaded_file() function. The file information is contained in the $_Files[] global array. The following link contains more information on file uploads.
Hope this helps.