I have access to a company\'s unique linked in ID and would like to be able to do a search for its job postings; however, the only company-related input for the job-search
I know this isn't the API but you might find this plugin that they provide to be useful:
https://developer.linkedin.com/plugins/jobs-you-may-be-interested?button-type-yours=true
Just put in your company name and it gives a nice widget with your company's jobs. Again, not really the API but I thought it might accomplish what you wanted anyways.