How to be hired from a website? Best ideas welcome ...

[YogaPants2441]

I've been trying for months to find a job that best fits me - part time, not very far from where I live and still fun. Tried my luck and send some covering letters and cv's and did not hear back ... I am sure that if I get an interview I will manage to convince the interviewers that I am the best fit for their vacancy. I am very selective - I apply only for jobs that sound as good match for the skills I offer and pay well. Pension scheme and private health care would be beneficial too. I mean decent pay.
I have a very good job currently. However I almost don't have time for my family - will be a dream to have much more hours with my children! To support them with their school work and play with them. Also, I am at the same position for 2 years now and do not find much excitement any more. Have being offered a promotion too - not too sure whether I would like to do it or not ...
How come that we do not hear from these web advertised jobs? I have the experience (may be not with the exact job specification, but transferrable skills). Not being funny, but they advertise them for months and they do not contact potential candidates too ...Anyone with tips from recruitment? Thanks!