You can reference the cells and use an if statement to determine the top of the block, in this case the top of the block is under two blank lines
(note I started in the second segment since your first line didn't start with two blank rows, so you have to do this manually or add a blank row to the top)
So if A6 and A7 are black we pick the top line
In cell B8 enter =IF(AND(A7="",A6=""),A8,"")
In cell C8 enter =IF(AND(A7="",A6=""),A9,"")
In cell D8 enter =IF(AND(A7="",A6=""),A10,"")
for as many cells as you need for each cell we move the right we move down one cell B8 to A8, C8 to A9, D8 to A10
Once your formulas are entered copy them down to the bottom of your data
You will have a whole bunch of blank lines, so copy Columns B to F( or where ever your sheet stops)
Paste special in a new sheet, You can then sort to remove the spaces
If you need to keep them in the same order, after you paste them add a column with numbers and sort out the spaces then sort by number.
If you do this a lot you may want to use the indirect function and maybe macros.