I bought my 74 coupe this past week. The car has been sitting parked outside for 17 years.

Dave, your problem is one that is not uncommon among sharks.  Go to the search icon at the top of the screen and do a search on door latch, you will find a list of old posts regarding the problem but there is not a "standard" way to get it open, various ways have been successful.  Try having someone to push on the outside of the door hard while you pull the inside handle, this may relieve the tension on the latch and allow it to open.  There is an old post by DaveM that has a pic of the latch that may help some.  The trick that opened mine was to pull as hard as possible (with pliers after removing the lock button) on the unlock rod then pull the handle.  Others have used a long screwdriver to push into the window slot and push down on the lever to open the latch.  Im sure others will chime in here as this is not an uncommon problem.  If you can get a long spray can nozzle into the door Id soak it with PB Blaster, sitting outside may have set up corrosion in the latch.

OK Dave, here is some additional information for you.  The fact that your outside door handle is broken and wont raise all the way may mean that it is has the latch mechanism partially engaged and preventing the inside handle from working.  See if you can roll the window down and use a coat hanger or similar tool to pull up on the linkage where the outside handle rod attaches or pull up on the flapper from the outside and then pull the inside door handle.  If that doesnt work with the window rolled down use a long handled screwdriver to push down on the latch lever indicated in this pic (this pic was borrowed from another forum so credit goes to the original poster, Durango-Boy on corvette forum and not to me)  If you push down on the lever, with some force, it should release the mechanism.  If your vette has the plastic water diverter over the latch, you may not be able to get to the lever.  Please let us know if any of these work and if so, which one, it may help other members in the future.