Can anyone give me advice on how to see a bit of Alaska in a short amount of time? I only have about 5 days to spend there, I'm on a budget and don't have my own vehicle.
Things I would like to do:
Fly into Anchorage - stay overnight? (as starting point to get to Den Nat Park)
Denali Nat Park - 1 1/2 days?(by bus from Anchorage? Stay in the Park?)
Fairbanks - 1 day? (from Nat park by train?)
Ferry trip - 1 or 2 days(Are there short routes or day trips you can take for the boating experience? How do I get to a departure point?)
End in Vancouver (what is the best way to get to here at the end of my Alaska trip?)
Any advice is much appreciated

First suggestion -- cut Fairbanks from the plan.

How to get to Vancouver? I don't know where you're coming from or going to, but I'd think on your schedule the only possible way to get to Vancouver in less than a day is to fly.

Without a car you will have even a tighter timeframe. You can do more in a shorter time if you don't have to rely on public transportation. You do not have time for Fairbanks. In 5 days, just plan on seeing Anchorage and getting back and forth to Denali Park- you will need 3 days for that, 1 each coming and going and the third for entering the park, via SHUTTLE bus, my min. recommendation is Fish Creek, reservations necessary. Only way to get to Vancouver is to fly. You can consider a Whittier- Prince William Sound tour from Anchorage, which can be a day trip.

Thanks for the responses!
After talking with my travel companion we are considering your advice to skip Fairbanks but we still really want to do a short ferry trip. The problem is we don't want to be stranded without public transportation.
We are arriving in Vancouver so I am thinking now of maybe taking the ferry from Prince Rupert to Juneau (I think this is overnight/1 day).
Can we fly from Juneau to Anchorage and then go on to our Denali plans? Is there a bus or train route from J to A or would that take too long? (We're still trying to work within a budget)

The only time saving way between Juneau and Anchorage is to fly. Ferries take TIME, which in my opinion you are not budgeting enough of. Clearly- without a rental car, your best bet is to fly into Anchorage, take the train to Denali Park- at least 2 over nights are needed- 3 is better, make an overnight stop in Talkeetna, then train back to Anchorage. That's about it within 5 days using public transportation.

If you really want a short ferry trip, grab the Valdez-Whittier leg (getting to Valdez might be a problem), a perhaps a Seward-Homer stretch (which has bus connections on each end), or a Whittier-Valdez-Whittier trip.

It would be logistically difficult and extremely expensive to add a Southeast AK ferry leg on this trip, i.e. expensive to get to Prince Rupert and to fly out of Juneau.

IMO, tho, you'd be see more by doing the full day Kenai Fjords tour.