What kind of capacitor blew up in my old IBM monitor?
What you have there are metallized impregnated paper capacitors made by KEMET.

Here is a datasheet of the parts.

The most important thing you have to look for is the capacity rating which should be on the top of the capacitors, which we can't see in your picture (see page 9 of the datasheet).



With the added information, I'd say this is your replacement part: PME271MD6100MR30 

This is a X1 rated capacitor, but X1 > X2 in terms of safety, so it should be fine. Actually - scrap that, Mouser links to the wrong datasheet.

Make sure to measure the distance between the legs, this one has 22.5mm which seemed to be the spacing on the old ones based on the information of the datasheet, but better measure that.



For a spacing of 20.3 mm, the PME271M610MR30 sounds right.