My $.02
If the chain got so bad as to have actually broke I fear that the cogs may be toast on at least the favorite gears and he'll probably experience skipping in the smaller cogs with a new chain.
Maybe I'm wrong. The only sure way to know is to try to put a new chain on and to adjust the derailleur and hope for the best.
If the cogs are worn it's not going to be nearly as cheap to replace the Helicomatic cogset as it would be with a modern cassette or older freewheel. I wouldn't bother. I'd ditch the whole rear wheel and look on Craigslist for a used replacement 27" wheel. That shouldn't cost very much at all if he shops around. Maybe his LBS will hook him up with a good used deal. It might even come with cogs/cassette that works with his system. As Sheldon said, these Helicomatic hubs are losers. Not only are they expensive to find new cassettes but they have bearing issues as well and conesets are unobtanium. I bet the OP could sell the old wheel for as much if not more than the cost of a replacement if the hub and bearings are OK. Perhaps his LBS will help him with this too.
If the OP isn't up to doing the work himself I can't see why he can't get the work done at a decent LBS using a used wheel and selling the old one for much more than $100. Perhaps much much less. I see wheels on CL all the time for half that price if he can do it himself or find a friend who is local who will help him.
I'd fix it and ride it or fix it and flip it. It's not worth much broke. The bike is worth fixing in any case IMHO. Just dumping it and buying a low end bike is not a good idea either as far as money is concerned and you'll have a low-end bike in the end. Spend a little money on a new/used wheel if a new chain doesn't cut it and if that is all that is wrong with the bike then he's got something fairly decent.
Perhaps he can recoup all or most of his losses selling that Helicomatic Object when he is done.