Transform Table Data With A Formula

I have a table with data and I want to transform the data in table 1 to the format in table 2 with a formula. I want to change the table format since I have data with 12 000 rows in table 2 format. I haven't been able to find any formula that works, so I will try to explain my problem

Table 1: How the data looks like

Account number
Account Name
Description
2013-01
2013-02
2013-03
2013-04
2013-05

4010
Bank
Sales
0
10
0
5
0

[Code] ........

Table 2: How I want the data to be transformed

Account number
Account Name
Description
Month
Amount

4010
Bank
Sales
2013-02
10

[Code] ........

1. The same accounts are used several times, but with different description or months.
2. All "0" values are eliminated in table 2.

My first thought was to use a pivot table, but I can't use it on sheet 1 since each month become a separate value.

Maybe there are some setting in pivot tables that makes it work, but I would prefer a formula to solve the problem.