How to Get Refund from South West Trains?

No, I'm afraid you were told the truth.

You are not eligible. You have a pass so you didn't pay anything extra for those specific trips. If you were eligible they would refund a portion - depending on the total delay each way - based on the amount paid.

If the first delay was out of SWT's control you also may not be eligible. I work in the industry (total over 30 years) and have never heard the expression "system emergency" so have no clue what that means.

The trains from London Victoria are run by Southern, not by South-West Trains.

South-West Trains run from London Waterloo to Portsmouth, and are generally faster because the journey is shorter.

Nigel, thanks for confirming the situation. It just doesn't seem fair that we "wasted" a precious vacation day without any compensation, especially as this was the greatly anticipated location to explore my husband's family roots.

The system emergency (as we were told by other passengers) was that someone threw themselves in front of a oncoming train.

That is tragic indeed, and I can certainly see why they had to shut down the line for a time.
Similar situation in Germany when we missed a connection in Duisburg because our regional was delayed arriving for what, the DB travel agent said, was "someone on the tracks". I hope it was not a similar tragedy, but it turned an 8 minute connection into a 2 hour one. When we boarded the connecting train, the conductor apologized for our delay and ordered us a cup of coffee from the snack cart. I was quite frankly stunned.