How to define multiple ranges with AVERAGEIF().

Hi all!
I have a little problem with a formula in a work document.

It is a document that shows figures for each day of the year with week, month and year total summaries. Some columns in this document calculates averages.

For the Weekly summaries i am using the following formula:
=IFERROR(IF(COUNT(B1,B4,B5,B6,B7,B8,B9),AVERAGEIF((B1:B4:B9),"<>0"),0),0)

This is for two reason:
1. I don't want the #DIV/0! error to be displayed when the average is calculated for empty cells so that the week, month and year totals always displays values.
2. I want "0" and blank cells to be excluded from the calculations.

The problem i have is that when a week spans two months, the RANGE in the formula must be split into two (because the month summary is in between) and for the "IF(COUNT" part in the above formula i can just use commas to define each cell instead of two ranges.
BUT, i cannot find a way to define multiple cells or ranges with "AVERAGEIF". I tried using commas as with COUNT and i also tried using it with "AVERAGEIF((B1:B4;B9)" which gave an error and suggested me to change it to "B1:B4:B9" which doesn't calculate correctly.

See the example file attached.

I really hope someone has a good solution or info to point out what i might be doing wrong
Also, if suggesting an entirely different kind of formula, the important steps are:
1. Calculate Average excluding "0" and blank cells.
2. Show a value of "0" if an error is the result.
3. Be able to define multiple cells or ranges.

What if he had multiple ranges he wanted to average? How would he go about do that? What if he had more data he wanted to get averages on in columns C & D? Thanks