This depends on your definition of peripheral devices. A computer certainly does not require I/O devices such as displays, keyboards or printer to function, although most will be designed to interact with the world to some extend.
A traditional CPU requires additional parts, such as memory chips, to function, but micro controllers or more modern system-on-a-chip designs offer more or less complete solutions within a single chip: volatile and non-volatile memory, video, network, and processing cores.
These devices are designed to function without, or with a minimum of low-cost, typically passive, additional electronic parts. Whether you'd consider such a system one with or without peripheral depends on your definition of peripherals though.
can a computer function/work without ac current
No, but it won't function without one.
To power your computer without a battery
No, a computer uses RAM (Random Axcess Memory) to function. RAM also determines the speed of you're computer; the more RAM the faster he computer.
The hard drive
There are no disadvantages of computer hardware, because without it, the computer would not be able to function, or even exist for that matter!
Yes, this is an internal function of the computer. You need a writable cd and the file on your computer.
Yes, it is. Because it is outside the computer, is a secondary device because your computer can function without it.
They are the files that your computer call on to start up, or "boot." without these, the computer cannot function properly.
The basic function of a computer case is to protect computer components from damage. The secondary function is to easily move the computer components, such as the motherboard, hard drive from one place to another. Computer.
USB
Absolutely... except for the fact that the computer will not be able to keep the software up-to-date, the computer will still function without the internet.