While composing this question I found an alternate method of linking groups
of cells between workbooks in the help file. I'm submitting this question
anyway, because I would like to know what caused the inconsistant results
with the method I was using.
If you found this question during a search and are having problems linking
groups of cells between workbooks go to the end of the message for a possible
solution which I found in the Excel 97 help file.

I've been having a problem with both excel 2002 and 97, I only have access
to 97 this evening.
I'm linking a portion of a column from one workbook to another. The number
of cells linked between workbooks is the same, but the column and row
references can differ.

The problem is that I'm using the same set of keystrokes each time I create
a link, sometimes it works, other times the cells display #VALUE! instead of
the data from the linked workbook.
Here are two examples using the actual cell references. The first worked
correctly, the second gave me a #VALUE! error.

1. This instance displays the CORRECT data:
The two workbooks are the DisplayBook and the DataCollector, both are open.
I select cells $G$3:$G$22 in DisplayBook
I press the "=" key
I select the DataCollector book
I select cells $F$3:$F$22
I press Ctrl Enter (Ctrl Return)
I'm taken back to DisplayBook and I see the correct data from the
DataCollector workbook in cells $G$3:$G$22.
All 20 cells ($G$3:$G$22) show the following link:
=[QIIG_DataCollector_2006.xls]QIIG_DataCollector_2006!$F$3:$F$22

2. This instance displays #VALUE! instead of the correct data:
The two workbooks are the DisplayBook and the DataCollector, both are open.
I select cells $G$42:$G$49 in DisplayBook
I press the "=" key
I select the DataCollector book
I select cells $F$49:$F$56
I press Ctrl Enter (Ctrl Return)
I'm taken back to DisplayBook and I see #VALUE! in cells $G$42:$G$49.
All 8 cells ($G$42:$G$49) show the following link:
=[QIIG_DataCollector_2006.xls]QIIG_DataCollector_2006!$F$49:$F$56

The cell formatting is the same in the linked cells.

Any Thoughts?

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Method for linking groups of cells between workbooks that I found in the
Excel help files:
The two workbooks are the DisplayBook and the DataCollector, both are open.
I select and copy cells $F$49:$F$56 in DataCollector
I select the DisplayBook
I select cell $G$42
I paste special and click paste link
The correct data fills the 8 cells $G$42:$G$49
The 8 cells ($G$42:$G$49) show the following links:
=[QIIG_DataCollector_2006.xls]QIIG_DataCollector_2006!F49
=[QIIG_DataCollector_2006.xls]QIIG_DataCollector_2006!F50
=[QIIG_DataCollector_2006.xls]QIIG_DataCollector_2006!F51
Etc...
=[QIIG_DataCollector_2006.xls]QIIG_DataCollector_2006!F56

Here is the actual help file I found:
CREATE A LINK TO WORKSHEET DATA ON YOUR INTRANET OR THE INTERNET

1 Open the workbook on your intranet or the Internet that contains the data
you want to link to.
2 Select the data in the workbook, and click Copy on the Edit menu.
3 Open the Microsoft Excel workbook where you want to create the link.
4 Click the upper-left cell of the area where you want to see the linked data.
5 On the Edit menu, click Paste Special.
6 Click Paste Link.

Note To create a link without opening the workbook on the Internet, click
the cell where you want the link, and type an equal sign (=) and the URL
address, followed by the location in the workbook. For example, type
=[http://www.someones.homepage/file.xls]Sheet1!A1
or
=[ftp://ftp.server.somewhere/file.xls]Sheet1!MyNamedCell