I know there are trains from Malmo to Copenhagen.
What about Helsingborg to Copenhagen? I found a website with trains, but I couldn't figure out the pricing. Suggestions?
Or what about transportation from Helsingborg to Malmo so that I could get the train to Copenhagen from Malmo?
Any help appreciated.

Here's one way:
Take the ferry from Helsingborg (the Swedish town) across to Helsingor (the Danish town). This doesn't cost much - I think something in the neighborhood of $5. It's about a 20-minute trip.

Then take the train from Helsingor to Copenhagen. I don't know how much this cost, because I had a Copenhagen Card (the 3-day version) that covered this.

On the other hand, you can take the train from Helsingborg to Copenhagen - I think that is more expensive.

Sorry I can't help with the costs. Take a look at railsaver.com and enter this itinerary, selecting the option "Only if a rail pass saves me money". However, it's quite possible the prices will be off by a few dollars.

If you are looking at the www.dsb.dk site, then you could email and ask about the fare.

I have a related question. Do the ferries between Helsingor and Helsingborg take cars as well as passengers?

Yes they do

There are three ferry services between Helsingborg and Helsingør, all with frequent services:
www.scandlines.se;
www.hhferries.se;
www.sundbusserne.dk (no cars).

Thanks, Helen and Geoff!

I did it last year and it was not very pricey without a car. The ferry give phenominal views of the castle in Denmark.