Chain skipping with new chain and freewheel I've recently (last 6 months) begun riding again after many years away and have begun updating components on my bike (a mid 80s era Fuji).  After replacing the rear wheel and freewheel I developed a problem with the chain slipping.  On a 7 speed freewheel, the 2 highest gears run fine, the 3rd gear slips somewhere between the 10th and 15th turn under load (but not when hand cranked with no load), the 4th gear slips so badly under load that it won't engage (again, I can't repeat this by hand cranking with no load), and gears 5 - 7 work fine.  Thinking that it could be caused by the old chain I replaced it but the same conditions still occur.

Additional information: 

All cables have been recently replaced.
The rear derailleur was replaced about 1 month ago.

Any ideas would be greatly appreciated.

Thanks.
You don't say what derailleur and shifter you have, but if they are an indexed Campagnolo system the spacing they're designed for is different in the middle of the cassette to the ends. I had exactly these symptoms with a 10-speed Campagnolo cassette on a SRAM bike.

You will have an array of problems if the mech and shifter's idea of cable pull do not match, particularly with an indexed system.

You will have exactly this problem trying to use any non-7-speed shifter/mech with a 7-speed system.

You can also get these symptoms if the B screw of the derailleur doesn't leave enough clearance between the top jockey wheel and the sprocket on the cassette, but it is more usual for this to affect the easy gears.