I have the same issue with my 1996 E320, remote range about 3, 4 feet. New battery no help.

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1996 E320 since 1/16/08, 171K miles as of Feb 2011

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1989 300CE - R.I.P. Dec 29 2007
Other MBs (sold): 1992 300E-24 - 1979 350SLC - 1984 230E - 1990 300CE