Consolidate (or Remove Duplicates) on range with 4 columns, and count totals for 1 column only

[lamensterms]

Hey,

I'm not sure if this is a unique task or I'm just not using the right search terms when Googling... hoping to get steered in the right direction.

My situation... I regularly have to process poorly collated data (extracted from software that doesn't have very good reporting feature). The data is part lists for steel fabrication. The raw data is a formatted as a single row for each instance of a part, that is if I have 4-off of "part 1", there will be 4 rows, each with "part 1" showing a quantity of 1-off. I could use the Consolidate feature if I am working with only 2 columns, but I am working with 4 columns, and I only want to SUM 1 column's data. Sorry for the poor explanation

Does anyone know of a good method to achieve this? My current method works quite well, but is a bit tedious and I am hoping there is a more efficient way

What I've got:

What I need:

 

[Fluff]

Lots of functions allow a formula to spill across a range.