Complex nestig of match, sumif, vlookup, hlookup?

[notanexcelguy]

I have a spreadsheet and I need to write a formula to do a couple things.
1. Search a range of cells on a separate sheet, same workbook, and find the columns with headers rows within a specific month
2. Once the correct columns are found, then I need it to look at the values below.
3. For each value in the correct column I need it to look horizontally to find a second value
4. If the second value is not found, I want it to disregard
5. If the second value is found I want to add up all the values where the second value is found

I am new to writing this type of formula and could really use some help here.

Thanks in advance

 

[notanexcelguy]

Column B Column E Column F Column G Column H Column I Column J Column K
Name 7/8 7/15 7/22 7/29 8/5 8/19 8/26
Not2ndValue 40 40 40 40 40 40 40
2nd Value 40 40 40 40 40 40 40
Not2ndValue 40 40 40 40 40 40 40
2nd Value 40 40 40 40 40 40 40

So I want:
1. Search for all columns with dates w/in the month of July
2. Look at each value in the columns from Step 1, and find the values that have the "2nd Value" in the same row
3. Once all the values w/2nd Value are located, sum the values from the columns in July

Desired Formula Result from this table: 320

Unfortunately, I am building inside of someone else sheet full of macros and I cannot change the layout. Column B Column E Column F Column G Column H Column I Column J Column K
Name 7/8 7/15 7/22 7/29 8/5 8/19 8/26
Not2ndValue 40 40 40 40 40 40 40
2nd Value 40 40 40 40 40 40 50
Not2ndValue 40 40 40 40 40 40 40
2nd Value 40 40 40 40 40 40 40

So I want:
1. Search for all columns with dates w/in the month of July
2. Look at each value in the columns from Step 1, and find the values that have the "2nd Value" in the same row
3. Once all the values w/2nd Value are located, sum the values from the columns in July

Desired Formula Result from this table: 320

Unfortunately, I am building inside of someone else sheet full of macros and I cannot change the layout.

 

[notanexcelguy]

Here is a .gif of my spreadsheet, it may help with the data layout. Sorry learning the ropes of posting questions.