It seems that "too many inquiries" is a recurring reason for credit denial. Therefore, stop applying. Four doesn't seem like too many to me, especially if the creditors are pulling from different CRAs, so I suspect there are other inquiries on your CRs that you haven't listed.
If you really need a credit card, pick a card that's easier to get, such as a student card (if you're a student). The best student cards now are Discover it for Students and Capital One Journey.
There's no guarantee that a CCC will only use EQ - if you're borderline, even those that typically pull EQ may double or even triple pull you. What's on your other CR that's not on the EQ? What are your fico scores? Income? AAoA? Baddies? Need a lot more information - will this be your first CC? Try researching the shopping cart trick with store cards on the forums. But if you do, don't get a million store cards, just get one or two to help build history, which will allow you to get a proper CC in the future. Also, you may have to take the secure route - BoA seems to have popular secured CCs.
