Keep in mind that police cars are run 24/7 and they are usually not treated very well.They do however recieve maintnance on very timely manner,.......usually every 30 days. How many miles on your car? Try a simple tune up,...........plugs wires and such. Thank You, Rob in PA.
It sounds like it could be a misfire in the transmission. surely you know how big the transmission is there is a part of that which relays to the spark sensor if that misfires you might experience a normal accel until you change gears then the car might shut down or not respond to the gear changing all together if that's your problem then get some bosch p4 spark plugs they deliver more than enogh power, of you can take it to a chevy dealer and drop 80.00 to let them take a close up look at your transmission, you might wanna get a rental lined up cause it'll take at least three days. other options can include a newer transmission I think the specs from a 96 impala match the caprice if thats true then definitly the 96-99 monte carlo but bear in mind if you pull from a monte carlo expect to tweek your trans cause theirs is running off a V6 not V8 therefore the ratios are not optimized for a caprice you can get ratio specs from any chevy service center that has been in business since 1996