The "Power" limit comes from the amount of cards (and level of the cards) that you own as you need a minimum amount of power for each tier level.
I am a relative newbie too - and it would have taken ages to play enough to buy enough cards to get out of bronze. But then I discovered that you can rent cards.
They are very cheap and start from as little as $0.001 per day per card (that is 1 DEC per card per day). Within 36 hours I had "won" enough games to cover the DEC costs of renting cards for a week. Plus, with the cards I had rented I had enough power to get into the silver league (and you also earn more DEC per win in the higher leagues, along with 2 cards per daily quest, etc). I would really recommend that you have a look at this. Worst case I would just rent out a "Goblin Mech" for a short period. It will help you in your current league and will let you work out if renting is for you.
The URL below is the article I wrote about renting cards in case you want to read more.
RE: Splinterlands: Newbie to Rich? ( First day of playing Splinterlands ) (REPOSTED: reason below)