what conditions force him toaccept captain william Prichards offer

Gulliver's business ventures (his medical practice) were not going well. Thus, he accepted Captain Pritchard's proposal.

I removed from the Old Jewry to Fetter Lane, and from thence to Wapping, hoping to get business among the sailors; but it would not turn to account.  After three years expectation that things would mend, I accepted an advantageous offer from Captain William Prichard, master of the Antelope, who was making a voyage to the South Sea.