Dyeing yarn?

I got hold of some yarn that was made in the late 1960's. It's 60% acrylic and 40% rayon. It's called "Dazzleaire". I have 6 skeins of white from the same dye lot. I also have 4 skeins of white with a problem. It looks like they just sat on a shelf gathering dust and the outside of the skein is somewhat discolored. I made a swatch and bleached it. This help some.

Do any of you know if this kind of yarn would take a white dye? Any other suggestions on getting our the off white color and getting it back to white?

What I want to do is make a sweater coat out of it if I can use all the yarn. Any suggestions would be very helpful!