Nikon D70 DSLR Flash will not Fire why?

Camera just arrived today, using Nikon 35mm f=1:2.8 Manual Lens focus is in Manual how do I test built in Flash to see if it works I attached a Vivitar 283 Flash works good when using pop up flash shutter will not take any pictures. I need real help here.

The D70 is a pretty old camera for a digital camera, but still a decent performer. Chances are, the built in flash is not functioning properly. Nikon cameras of that vintage have a problem where a spring contact becomes dislodged within the flash mechanics causing the flash to fail. There are articles on the web that detail how to fix this if this is the problem. Do a search for fixing the D40 pop up flash (flash mechanism is roughly the same as the D70).

A broken flash on the D70 isn't a big deal. Since you already have the Vivitar flash, just use that. I rarely use the pop up flash on my cameras since you can't bounce the flash.

My bet would be that the flash is dead. The camera is waiting for the signal from the flash that it is ready to fire but that signal is not forthcoming. As a result the shutter will not fire.
Pop-up flashes on DSLRs are so utterly useless that I wonder why they bother fitting them. They have a puny output, can't be bounced and sit so close to the camera body that any large lens/lenshood casts a shadow.
You Vivitar 283 gun is OK but it doesn't make use of your camera's auto flash functions. Additionally some older guns use very high trigger voltages that may fry the electronics in your camera if you use it too frequently. You may want to read this:
http://www.instructables.com/id/Taming-the-high-trigger-voltage-of-the-Vivitar-283/

For the price of repair you could buy a decent entry level Nikon speedlight, eg the SB-300

Because you bought somebody elses old, used headache.

M mode, 1/125s, f/16. If it still does not work, focus manually. If that still does not work, flash is broken.

That camera is quite old, so you might expect it to have a few faults. Probably nothing you can do at home to fix it (but see the answer by Qrk), and any repair at a lab is likely to be expensive.

Let's start at the beginning. First, did you READ your camera's Instructions Manual? IF you don't have the D70 camera Instructions Manual, get one from the Internet and download it for free: http://downloadcenter.nikonimglib.com/en/products/214/D70.html (READ and follow instructions).

The D70 is still a fairly good DSLR but may require the correct "commands" to accept newer flash units, particularly from a flash manufactured by a different brand.

When you bought the flash, did you mention to the salesperson what your camera brand and model number is? Call wherever you bought the flash and explain your problem; or call Nikon USA and speak with one of their technicians and ask.

READ your camera's Instructions Manual and make certain you have the correct setting for using the built-in flash (it may be 1/200th shutter speed); it you're using something slowyr or faster, it may not work. READ your camera's Instructions Manual, and look for teh page on the index for Built-in flash.

Did you remember to remove the lens cover? Did you remember to raise the flash when on Manual Mode (by pressing the small button on the right side of the flash with a tiny lightning bolt symbol)? Are you using the correct shutter speed for flash while on Manual Mode (It MAY be 1/125th second OR 1/200th second; check with the cameras Instructions Manual)?

IF indeed the flash is defective/broken, it's not a "deal breaker" but you can always try to exchange it where you bought it from, or do without it altogether; I've had both of my Nikon DSLRs for several years, and even before that (even during the film era), I NEVER used my cameras' built-in flash; it causes pink eyes from humans and blue/green eyes from pets because the flash is too close to the lens, and the reflected light from the eyes comes back to the lens area, resulting in pink eyes.