Whirring Noise - Hard Start

Hi,



I have a 2003 Chevy S10 with about 77,500 miles on the odo. I’ve recently noticed a persistent whirring noise coming from (I think) the front of my truck. The rapidity of the whirring increases with my speed, but it goes away entirely when I depress the brake pedal. The noise is also present when I’l idling at speed.



Also, and I don’t know if this is related, my truck is taking its sweet time starting. I just replaced the battery as the old one died on me (right outside Wal-Mart, as luck would have it).



I would appreciate any ideas.



Thanks,

-James