There are a lot of dumb posts in this thread and some really uninformed people. You probably shouldn't be posting if you're not a computer engineer/electrical engineer/computer scientists.
First of all, I'm a senior in computer engineering which instantly gives me more credence than most of the posts in this thread. Second, I interned at Motorola for 3 months and at Intel for 7 months so I know the answers to your industry questions.
Your initial post demonstrates your misunderstanding of what the fields of engineering really are. Electrical engineering is fundamentally math and physics. Some of the corporations an electrical engineer can expect to work for range from Intel, AMD, and Qualcomm to embedded system engineers at defense contractors like Boeing, Northrop Grumman, and Rayhteon. That is just a range, there is more than you can imagine like government (NASA, NSA, department of defense) and consumer electronics (sony, motorola, samsung). You can do anything from programming, low level device physics, hardware verification, signal processing, and much more.
Computer science is on the opposite end of the spectrum. It is more about math and programming than physics like EE is. Job opportunities for CS students also have a wide range and depend on what you're looking for. One of the most desired positions is tools development. That means both internal facing tools and external facing tools. For external, think Microsoft, Cisco, and IBM. These companies make tools for users like Work and productivity applications for businesses. Conversely, almost all major companies have many, many CS grads for their internal tools. For example, Intel is currently a top 10 software manufacturer in the world not necessarily because of drivers but because they need computer science majors to create the software that their engineers are using. There are hundreds of programs developed for internal use only at Intel just so their engineers can do what they need to do to actually make the chips and verify them. I use Intel as an example but all major tech companies have similar needs. Other CS jobs range from verification at any hardware company (hardware is much more than processors btw, think consumer electronics, military, telecom, space, etc) and pure software companies like Google, Amazon, and eBay.
Finally, computer engineering is right in the middle. It doesn't focus on math or physics but more on logic and computer architecture. Focuses with a computer engineering degree are a little bit broader since it combines aspects of CS and EE. My favorite part about it is you can do a CS job or an EE job based entirely off what you enjoy. For example, my school doesn't allow CompE's to get minors in CS or EE because they are so similar. It does however, let EE students get minors in CS because it is a little farther from CS than CE is. You can do anything a CS or EE student can do depending on what technical electives you decide to take. The "core" compE curriculum consists of computer architecture, logic design, and low level programming. Major employers are Intel, AMD, Qualcomm, ARM, TI, and others. It really can cover the spectrum. I know people working at Microsoft/Google with a CE degree and people working at fabs at Intel with a CE degree. It is entirely up to you.
You seem to have the notion that CE students just do Verilog or VHDL when in reality, I'd say most CE students end up doing verification in C. Some CE students do use those hardware-y languages but there are many more doing a wide range of things.
Specifically, to answer your Intel questions, they hire a huge range of people. They don't care about your degree, they care about your skillset. You can interview for any position and as long as you know the subject matter, they'll hire you. They need software devs for tools, physics majors and EE majors for transistor level work, CEs for hardware design, EE majors for fabrication process. All you need is a skill set that lines up with any of that and you can work there.
BIOS engineers design the bios that goes on both internal motherboards used for testing and the spec boards that go out to vendors that can be tweaked.
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