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As long as you return a 404 server response code, you should be OK. If, however, you return a 302, you could end up with duplicate content issues.
You can use the Server header checker [webmasterworld.com] to find out.
Jim
HTTP/1.1 200 OK
Server: Microsoft-IIS/5.0
Cache-Control: no-cache,no-transform
Expires: Fri, 18 Apr 2003 15:10:30 GMT
Vary: *
Date: Fri, 18 Apr 2003 15:10:30 GMT
Content-Type: text/html
Accept-Ranges: bytes
Content-Length: 15875
Suggestion: Not to be flippant, but... Get a new server?
Until that becomes feasible, you should ask your hosting provider how to fix the problem. Or tell them to fix the problem, since it is their restrictions which prevent you from fixing it.
This will only become a big problem if you change a lot of file names or delete a lot of files. Otherwise, Google will never see your 404 handling.
There are several threads running around here which include (but may not be directed at) returning modified server headers using PERL, PHP, ASP, and CGI scripts. If any of those are options for you, they would be worth searching for.
Jim