I got my Computer Engineering degree in 2000, just about the time all the jobs went away, and have had a rough time getting in. I worked menial jobs for several years to try to make ends meet, all the while applying for all the entry-level engineering jobs I could find.
In Jan 2004 I started working for the company I'm with now. The first two years I worked through a temp agency, and came on permanent the first of this year.
I work for a research lab that's part of the University of Texas. Universities, and their associated labs, pay squat. I'm making about half what I expected to when I was getting the degree. My wife is a nurse, a profession thats notoriously low-paid, and I make about $.50/Hr. more than she does. We're scratching to make ends meet, especially since we both have student loans to pay off.
On the other hand, the benefits are good (like a week so for Christmas, while UT is shut down), and it's a very relaxed environment compared to the 'bleeding edge' technology companies.
Best thing about it is that we do R&D work for Navy and Coast Guard underwater systems. During the Gulf war, did you hear about the trained dolphins that they were using to hunt for mines? We made the training aids. We also make the hand-held mine detectors that the Navy divers use. But our biggest projects are sonar systems that detect and track divers and swimmers entering restricted areas. One group is playing around with unmanned underwater vehicles for something. We have an in-house dive team that dives every week or two (the team dives that often, but they rotate through the members. Individuals might dive every month or two). Mostly they do long swims at about 20, to test diver detection and tracking algorithms. They also do deeper dives (up to 130 or so) to reposition targets, maintain u/w structures, or occasionally to try to find tools and parts that have been dropped. Unfortunately all those dives are in Lake Travis in low vis, but at least theyre getting paid to get wet. Also, some of the Engineers get to do some traveling to test/set-up/maintain the systems were developing. Those guys usually take their dive gear along and do some personal dives while on the trips. I am going to be doing some of those trips soon.
So, there are jobs out there that allow Engineers to dive, and even pay them to do so, but they are few and far between. And if you are doing scientific/oceanographic research, dont expect to get rich. Im actually looking at getting a second job.
Oh, and one more note. At least where I work, its really difficult to get into the research labs if you didnt graduate from their university. The head of our division told me that I will always be looked down upon when it comes to promotions and pay raises because my degree is not from UT or a top 10 university. Im willing to bet that its the same with other university programs.
My advice would be to get the broadest Engineering degree you can, study hard so that you truly understand the concepts, and participate in as many internships as you can while in school, then look for a job that includes travel to some good dive spots. Just being willing to travel opens up some doors.
That's my perspective.
Oh, and here is another thing you might want to investigate. There are other professions, like Oceanographer, where you still get to play with a lot of cool u/w gadgets, and even help develop them. But, again, they don't get rich doing it.