Craftsman weedeater 316.970111 model//starts easy & runs for ten to fifteen seconds & dies like its out of fuel. has new primer bulb,fuel lines,spark plug.

I could not find your model based on the number you listed in your questions. Sears Parts Direct will have the schematics for your machine. Difficulty with starting the 2-cycle trimmer (especially if it has been sitting for 6 months or more) is common:

It is most likely you will need to service the carburetor. Today's modern fuels will, over time, gum up the carburetors and small passage-ways within the carburetor making the carburetor ineffective. Diaphragms will become stiff and ineffective. A carburetor rebuild kit can be a DIY project and are inexpensive. Common carburetors for the Craftsman is either Walbro or Zama. You will need to look closely at your carburetor to find the name and model for replacement carburetor parts.

You can also remove the exhaust or muffler to visually insure that the small screen (if applicable on your actual model) is clear of carbon build-up. Clean/replace and retry.

Before you rebuild your carburetor or remove the exhaust, try the simple things below:

1. Air Filter maintenance. Your air filter needs to be reasonably clear. You can clean with water/soap, insure it is dry and lightly oil and replace.
2. Replace your pre-mix fuel or determine that is no older than 2 months old. I know you have done this, but insure it is fresh AND is of the correct ratio (typically 23:1 to 40:1).
3. It appears you have done this, but if not Follow the fuel lines (especially within the fuel tank) any deterioration in the lines will allow air into the system which will contribute to a difficulty in starting. Fuel lines > 6-7 years old often need to be replaced.
4. Remove the fuel filter within the tank and clean by blowing compressed air through the filter and using soap/water.

Retry. These are the issues to about 95% of starting problems for 2-cycle string trimmers.