Have got the answer to this as had the same problem. Like your own page from your personal account then make your personal account admin for your business page. Go back personal account and click on settings (top right hand corner) select 'view as (business page)' or whatever it says. Then you will be able to search and like etc.
It's strange how fb do that isn't it Cherry? I wonder why that is? I did consider setting up a personal account linking to the business account, but I'm not sure how that would work. If I liked businesses using the personal account, they will probably like me back on that account, not on my business page. So I am still not reaching as many people as I'd like with my business updates. Unless you were to phase out the business account and use the personal account in place of it. Hmmm, nothing's ever easy!
Had exactly the same experience, had planned to like other companies also. A friend made 2 profiles for their company. A business one and a normal account so they could overcome the liking restrictions. May be an option to consider. Will be interested if any other suggestions though.
I have recently started a new business so have created a business page on FB linked to my personal FB page, to try to get word out about my business and attract clients. However, I am now coming to realise that business was pages can not Like other pages, or request friends etc. my plan was to Like other local businesses in the hope of them reciprocating, and us supporting each other.
I'm not sure how to go about this now, as I only have a handful of Likers and just not enough people are seeing my page.