1) No, it doesn't make you look foolish.
2) You'd look foolish if you didn't take advantage of resources and tried to be heroic. Time is paramount. Never forget that.
3) Nobody is going to actually do your job for you. They will just give suggestions.
4) Be prepared to trust the help you get and take it seriously. For whatever its worth, even if it doesn't answer your question entirely.
5) Asking for help stimulates discussion. You learn a lot, and its fun to discuss this stuff with people who like talking about it.
6) Involving others also means a pressure to get the task done quickly, rather than drag your feet over it in isolation and be buried in complications you don't understand.
7) In the end, there will always be a part you will have to figure out by yourself, you can get your kicks from that.
8) (Obvious but) Reaching out for help speeds things up exponentially. I just wrote to folks from my old lab last night about trouble I was having with some analysis (At PhdAdvisor's behest). I already got a reply from one of them this morning. The fact that he spent time with my stuff at 1 am last night makes me feel so thankful. And while I was sleeping, someone who knows this stuff helped move it forth a great deal.
One of the many lessons I've learned the hard way.