Maybe it is chainring wear. If the small chainring is used with the smaller rear cogs it will wear faster becuase of the sharp angle that the chain takes. The old chain could have worked because it would have worn together with the chainring. Take a look at these pictures on Sheldon Brown's website to see if that might be your problem. He is referring to rear cog sprockets, but the principle is the same.
http://sheldonbrown.com/chains.html
And Text quoted from that page:
"A new chain on a worn sprocket. Most of the driving is happening on the left side, where the chain first engages the sprocket. Due to the mismatch in pitch, the rollers in the part of the chain that is about to leave the sprocket is doing very little to push their teeth forward, instead, they are being forced upward by the slope of the teeth.
Since the teeth/rollers on our left are doing most of the work the load is concentrated on them.
In addition, as the roller follows its tooth around the sprocket it rolls up the "ramp," while under load. This promotes wear to the insides of the rollers and to the "bushings" they roll on. With a properly meshed chain, the roller only turns a tiny bit as it rolls onto and off of the chain.
Due to the pitch mismatch, the chain will not reliably mesh with the sprocket under load, and will tend to jump forward, skipping over the teeth."
You could also be having some "chain suck", which could also be caused by a new chain on an a worn chainring.
See this link for a discussion of chain suck:
http://www.fagan.co.za/Bikes/Csuck/
Chain suck could also be caused by the gunkiness of the grease and should get better with cleaning and relubing it.
Good luck. You have the right chain. HG73 should work with any Shimano 9s drivetrain.