I've never tried deleting rows, but below is what I use for hiding them;

Sub HideEmpty()
Sheet1.Unprotect
Application.ScreenUpdating = False

BeginRow = 20
EndRow = 1000
ChkCol = 1

For rowcnt = BeginRow To EndRow
If Sheet1.Cells(rowcnt, ChkCol).Value < 1 Then
Sheet1.Cells(rowcnt, ChkCol).EntireRow.Hidden = True
Else
If Sheet1.Cells(rowcnt, ChkCol).Value = "AutoHide.Sheet.Stop"
Then Exit For
Sheet1.Cells(rowcnt, ChkCol).EntireRow.Hidden = False
End If
Next rowcnt

Sheet1.Protect
Application.ScreenUpdating = True
End Sub

your approach is pretty good for someone who says they are
green...
How about trying this...
Sub erase_zero_rows()
Dim rCnt As Integer, iCnt As Integer
Dim iColumnToStart As Integer
Dim iColumnToEnd As Integer
Dim iRowToStart As Integer
Dim iRowsAll As Integer

iRowToStart = 4
iRowsAll = 69
iColumnToStart = 2
iColumnToEnd = 4
iCnt = iRowToStart - 1
rCnt = iRowsAll
With Range(Cells(1, iColumnToStart), Cells(1, iColumnToEnd))
Do While rCnt
If WorksheetFunction.Sum(.Offset(iCnt, 0)) = 0 Then
.Offset(iCnt, 0).EntireRow.Delete
Else
iCnt = iCnt + 1
End If
rCnt = rCnt - 1
Loop
End With

End Sub

do you want to delete the rows  where all the cells have zero value...

if the above said is true then find the answer below

Sub OM()
Dim lastrow As Integer
Dim lastcol As Integer

Worksheets("Sheet1").Activate
lastrow = Range("a65536").End(xlUp).Row
lastcol = 9 'because you are sure it is 9

Count = lastrow
i = 1
While (lastrow <> 0)
If (Range("A" & i) = 0 And Range("B" & i) = 0 And Range("C" & i)
= 0 And Range("D" & i) = 0 And Range("E" & i) = 0 And Range("F" & i)
= 0 And Range("G" & i) = 0 And Range("H" & i) = 0 And Range("I" & i)
= 0) Then
Range("A" & i).Select
Selection.EntireRow.Delete shift:=xlUp
End If
i = i + 1
lastrow = lastrow - 1
Wend
End Sub

Let me know if this solves your problem...

Find the answer below

Sub OM()
Dim lastrow As Integer
Dim lastcol As Integer

Worksheets("Sheet1").Activate
lastrow = Range("a65536").End(xlUp).Row
lastcol = 9 'because you are sure it is 9

Count = lastrow
i = 1
While (lastrow <> 0)
If (Range("A" & i) = 0 And Range("B" & i) = 0 And Range("C" & i)
= 0 And Range("D" & i) = 0 And Range("E" & i) = 0 And Range("F" & i)
= 0 And Range("G" & i) = 0 And Range("H" & i) = 0 And Range("I" & i)
= 0) Then
Range("A" & i).Select
Selection.EntireRow.Delete shift:=xlUp
End If
i = i + 1
lastrow = lastrow - 1
Wend
End Sub

You'll also need to stop the row increment, otherwise you bypass any
zero rows  that are consecutive.

code ...
While (lastrow <> 0)
If /condition/ Then
code ...
i=i-1
End If
i=i+1
code ...
Wend

I provided would not
work if there were positive and negative numbers on the same row that
could total 0.

Perhaps, then, this will work.
if abs(worksheetfunction.min(.offset(icnt,0))) + worksheetfunction.max
(.offset(icnt,0)) = 0 then

You got me 99.% of the way there. without i = i-1 before the End If it
would skip consecutive zero rows.