dfs mentioned the magical word which is networking. Very few make it through to a job with luck and being in the right place at the right time. On these forums you tend to get a very biased view of the job market with lots of tales of successes and the usual ranting that comes from those unfortunates. Most don't make it at all and give up. If you persevere then you are already ahead of the game. The amount of guys I bumped into that are unmotivated and are totally clueless about getting a job egged me on loads in my search.
Unfortunately few ever think about how to get a job until after they have completed their training, by which time they may have a CPL from here an IR from there and an MCC in a kingair cardboard bomber box done somewhere cheap next to the black stump. During the course of their training they would have bumped into no one of any significance in helping them get a job which surely is the whole aim of the exercise in the first place.
So how to network? Well some find it more natural than others. Firstly you need to recognise the fact that us pilots are actually a small minority in the scheme of things. Something like 1% of the population or less would be my guess. That means you just don't bump into airline pilots and training captains willy nilly. You need to seek them out. Certain airfield bars tend to attract some, some offer their services as FI's, others have their own aircraft and fly for fun. Others might do a bit of consultancy work on the side teaching things like MCC courses, JOC's, JOT's and any other acronyms you might like to think up. Others love a round of golf and can be found propping up the 19th. Sports clubs can also be a good source of meeting these folks. The aim of the game is trying to meet these people.
Op's jobs have worked for many in the past. Not necessarily being a despatcher but what about trying the huge number of corporate operators based around the smaller airfields like BOH, Bristol and the likes. There are also the medivac companies who might have an office job going that can be a good way to get your foot in the door whilst earning a buck. There has been many a pilot that has been tactically caught with their head in a jeppy plate just as the chief pilot walks past their desk which then leads to the inevitable "oh I never knew you had your flying licences"....
Finally if you aren't even getting interviews then ask yourself some tough questions? Is it anything to do with me? Did I go to cr*p schools - some airlines prefer certain schools and that is a reality that few like to admit. Is my CV cr*p or missing vital selling points like I am immediately available for work? Is my cover letter cr*p? The latter few points can hopefully be resolved with getting some professional advice. There are a couple of pilots offering these sorts of services that are discussed reasonably regularly here on pprune if you search them out. Never underestimate the importance of a cover letter. It can be a real selling point and get across why you have a connection to a particular country (if the job you are going for is away from your home), that you are immediately available etc etc. There are loads of good examples out there using google search of professional cover letters and formats including decent CV's as well that are uncluttered and fill less than 1 page.
Good luck.