As someone who was recently unemployed but has now found a permanent position in chemical engineering, I can understand what you are going through. The advice given so far is absolutely correct.
Networking is thrown around as a cliche, but it actually is the best tool. A website called LinkedIn actually helped me a lot in this. The site allows you to connect to people you know, and through branching out to their contacts you can find someone with a connection to a company you may be interested in. I highly suggest you make a profile on it an connect to whoever you can. This is, quite literally, how I found my current position. I am working in an electroforming department at a highly specialized reflective products company, a topic I have absolutely no experience in, with great benefits and pay. The real kicker is this: I never even applied for the position, or knew that it was even available. A local science-focused hiring consultant found my connection on LinkedIn, contacted me, and the rest is history. I did not know the specific consultant nor the company he worked for, but we had mutual connections and he thought my profile fit their wants. I am so incredibly thankful that I created a profile. I highly, highly suggest it, and it's free (there is a higher-level membership that you can pay for, but it's definitely not necessary.)
In addition, definitely be applying to almost anything you are tangentially qualified for. I nearly was offered another position when I applied to a company for one of their openings; the hiring manager was not interested in me for the position I applied for, but passed my information on to another manager who called me in for several interviews. The point is, it can never hurt to apply.
Keep trying, keep searching. With all of the internet resources as well as local ones, there are actually more jobs out there than you think, it's just that most people get so focused on one specific method of searching that they miss a whole bunch. Indeed.com is great for searching all of those internet job posting sites all at once, and my fiancee actually foound her job on Craigslist. Local newspapers still carry job postings, and always be on the lookout for a local job fair.
Good luck, I hope you are able to find something soon. Try not to get discouraged by rejections; just take their responses as constructive criticism and use their comments to tweak your resume and interview style for the next opportunity.