I will bet that your chainrings are just fine, unless the teeth have been worn down to pointy little hooks. (In which case, you have some nice circular saw blades there!)

No, you have a worn chain. You say that the bike and chain are seven years old, but you did not mention mileage. If the bike has only 3 or 4 000 miles, then the damage is not great...

First you'll need the check the chain for "stretch." Place a 12" ruler along the chain so that a pivot pin is neatly bisected by the 0" mark. Hold steady, and sight down to the 12" mark. It should neatly bisect another pivot pin. If the pivot pin is past the 12" mark by more than half the diameter of the pin, REPLACE the chain! Wait any longer, and the stretched chain will wreak havoc on the Shimano Hyperglide cassette's ramps and cut-outs. If you replace a really badly stretched chain... say, 1/8" or more, the ruined cassette will jump and skip so much as to render the bike unrideable.

NOTE: The metal of the chain does not actually stretch... friction and dirt wear the pivots, and elongate the pivot holes... microscopically. a few microns of wear, times 110 or more pivots, equalls 2, 3, 5 or more millimeters of elongation.

This was never much of a problem in the old friction shifter days... Once the chain began to drag the ground, it was time to replace it, no harm done. Now, though, it takes very little elongation to ruin a drivetrain.

Positive NOTE: Chainrings don't suffer much from chain stretch. They'll work fine, even worn down to little pointy hooks... until teeth begin to break off!

If the chain is as bad as I think it is, here is what you will need to do:

NOTE: This is not an expensive bike shop repair, if you lack the proper tools or experience. No dishonour. Take it to them. Watch and learn. Buy the wrench some lunch. They like burritos.

Otherwise, all you will need are:

Chain breaker, chain whip or a 2' length of old chain, and a Shimano lockring tool. This is perhaps $20 worth of tools.

Replace the cassette with one of the same configuration, for $25 to $40, then replace the chain with the best one you can afford, another $21 or so. Lube the chain, and ride.

Check the chain length each time you lubricate it, and replace it at 2 000 miles, even if it does not appear to be worn. Otherwise, you'll be replacing chains and cassettes every time.