Well, I don't normally suggest travel agents, but this might be one of those cases!
Amtrak goes from Seattle to Amtrak (lovely trip). But from there, IF there's a train that gets up near Alaska, you'd have to travel by VIA, Canada's railway (I've heard their trains are AMAZING). But I can't tell by a quick look at their website if they get near Alaska. Oh wait, when looking at a site I mention later, I noticed that Prince Rupert is either in Alaska or is right next to it, and it looks like VIA goes there, which could be a springboard into Alaska (or actually in it...can't believe how incredibly stupid I am coming across here regarding geography).
Another aspect is...is it just you? Do you have a LONG amount of time to get there? Is there a specific part of Alaska you want to see? Do you just want to tour wherever you can?
A friend of mine priced out Amtrak to Vancouver, then VIA over towards Detroit, and it was seriously expensive. (not the to Vancouver part) So the train travel could get VERY expensive, especially if you're going for a sleeper car.
You might want to really look at the cruises out of Seattle or Vancouver, to really see how expensive or inexpensive they might be (especially since they include food and entertainment). But that would only work if you don't have anything specific in mind to see.
Oh, and if you have a long time for vacation, and don't mind roughing it to a certain extent, Alaska has an extensive ferry system that intrigues me.
http://www.akferry.org/ Ooh, and it looks like it leaves from Bellingham, WA.