I recently went through the shutdown of a startup and also had to find a new job. This was my first time seriously job hunting in 10 years as I got my last few jobs in a variety of ways that were easy. So I did what seemed to make the most sense -- launch up LinkedIn Jobs and started applying.
Out of 20+ jobs I applied to on it, I heard back from basically none. 1 company responded, but was a very quick "not a fit" without even a phone screen.
I got a total of 3 interviews, where 2 were friend referrals and 1 was through a new job matchmaking startup. (Won't name it here in case it's mistaken as advertising) Fortunately for me I landed 1 of them.
So my issue could be that no one really checks these LinkedIn job applications, which isn't related to your issue.
I'd also like to point out that the shift in technologies in just the past 3-4 years have been huge, among startups especially. Your skillset may not be up to date with what companies look for now if you had been with the same company for 5+ years.