It doesn’t. You were pre-approved to receive the offer of credit, not for the card itself.
Don’t worry about opening new accounts, just focusing on making timely payments that are more than the minimum, and save up to buy the computer with cash once you’ve paid down your credit card.
I’ve had two Chase Visas with no complaints so far except that they send you lots of “convenience checks” every couple of months. However, I don’t think that transfering the balance to the other card will help your credit score much because they look at your total debt/total credit line, but if you can save on interest it may be worth the balance transfer fee.
Actually, asking for a credit line increase can hurt your credit. I shows up as a “hard inquiry” just as if you applied for a new card.
Hold onto your $500 until you know that you are approved for a gas card and what the limit is. If you get declined for that then you can use the money to open a secured card. Charge one tank of gas or one bag of groceries each month on whichever card you get and pay it off immediately.
You may also want to consider holding onto your $500 anyway. One mistake many people (myself included) make when trying to pay down debt is throwing everything you have at it. Then when an unexpected expense pops up you have to go into more debt to pay for it. Having a cushion (or better yet a Freedom Account) can reduce your vulnerability.
The problem I have lately, is all the advertisements that tend to equate credit-card companies as Evil Incarnate™ and how you can reach financial nirvana by telling them to stick-it as far as ever seeing their loans paid back.
Unfortunately, their is a decided ignorance on the part of many people as regards credit, money and banking and it’s arguable that competence in these areas is the most important skill we can teach to the young folks. Our social/economic system here in the US is skewed in some ways, where folks incur huge sums of debt early in life/career and hope to pay them down through higher level jobs/pay.