I thought I understood the dice pretty well but I'm unsure of this one.

The roll was 1 Triumph, 1 Failure, 1 threat, 4 advantage in a combat check. Since there were no actual success symbols this is a failed attack?

If I'm reading that right, no damage would result, but you would still get to use the Triumph and 3 net advantages for something, just not damage or crits? At first I was wondering if the Triumph could make the attack successful since I don't see where a failure cancels a Triumph and a Triumph equals a success. (but as I was thinking more about it typing this up, I think the triumph doesn't get canceled, just can't be used for damage or crits, but since there was no actual success symbol the damage attack was not successful?)

To clarify one point; a Triumph does not equal a success. A Triumph gives you a success as well, but it exists separately from the Triumph effect. Similarly, a Despair gives you a failure into the bargain. The success/failure element can be cancelled, but the Triumph/Despair cannot.

So, in your example, the failure cancels the success from the triumph, and the threat cancels one of the advantages. The attack fails, so there won't be any damage or crits done. However, the attacker still has a Triumph effect and three advantages to use. The attacker could, for example, upgrade the next allied character's skill check (with the Triumph) and add a boost die to it (with an advantage), while taking an extra maneuver themselves (2 advantage). This could represent flushing the target out of position, making it easier for an ally to attack them, while also buying time for the attacker to reposition.

The Triumph also counts as a Success, which is cancelled by the Failure (net 0 successes, so a failed combat check).

Triumphs and Despairs are never cancelled (though the Successes and Failures that they contribute to the pool can be), nor can they cancel each other.

In the case of your example, the Triumph could be used for a narrative effect, or another result not dependent upon a successful attack.