How can I open a corrupted PostgreSQL v9.1e database which has data that was added after it was last backed up?
Assuming your tag is right and this is a Progress, not a Postgres (as in the text), database you can try forcing your way in. However, backup beforehand! A forced database will be marked as forced and might never work again.
That aside, force might be a lifeline and the way to enter the database to dump it's content.
Here's a longer article about the force flag (-F).
Of course, you will need to fully understand the bits and bytes of the file internals, which "might" be a prohibitive factor. In addition, there is no guarantee that the corruption did not affect the 'new' data you are looking for, so even if you manage to magically get the file to open, you might lose some or all of the new data anyway.
The bottom line is that it all depends on how important that data is. If it's worth 3 billion dollars, or holds the evidence that will get you out of a life sentence, than go for it. It might take you many years though...
If not, I suggest you swallow the loss, minimize your damages, and increase your backup frequency so that next time it will hurt less.