Man, the Brooklyn Cruise Terminal sure is inconvenient!

If you want to go the cheap route, take the 6 train from 103rd/Lex to 86th and transfer to the 4 or 5 train to Borough Hall, Brooklyn. Then take the B61 bus as described on the BCT web page. You'll have to schlep your bags on and off the subways and buses, though, and walk a ways from the bus to the BCT, but it'll only cost you $2! Also, if you're going on a weekend, be sure to check the service advisories.

Getting from the BCT to LGA by bus/subway is similar. Take one of the buses to the F train, then take the F train through Manhattan out to Jackson Heights/Roosevelt Ave in Queens. From there you get the Q33 bus to LGA. Total cost = $4. Again, if you're going on a weekend, be sure to check the service advisories.

If you have two heavy bags, I'd suck it up and take a taxi, which will be much, much more convenient and almost certainly faster. Don't expect it to be cheap, though.