I am working on the genealogy of Ingalls and have found numerous
listings.  However, the location of Shirbeck, Lincolnshire, England
and Skirbeck, Lincoln, England are listed throughout the family
members. Are they the same or completely different locations?

This may be of interest:

"Here she pursued her studies under the guidance of [her father] the
rector of Shirbeck [a misprint for Skirbeck], of her uncle, and of her
French tutor..."

http://etext.lib.virginia.edu/bsuva/euromag/1EM.html

There is a Skirbeck in Lincolnshire, England.  Frequently Lincolnshire
is abbreviated "Lincoln", but they are one in the same.

You can see a map of Skirbeck here: http://tinyurl.com/3oms8 

There is no "Shirbeck" town or city in the United Kingdom, and this is
most certainly one in the same town.

If your family is from this town, here are some pictures of churches
located there that may be of interest: <a
href="http://www.bostonuk.com/gallery/neilwright/">http://www.bostonuk.com/gallery/neilwright/</a>.
 The website also includes a detailed history of the area.

You can also o a full-text search of a History of Skirbeck and local
towns <a href="http://www.hti.umich.edu/cgi/t/text/text-idx?sid=d28ca9e4123a83d8f7943c3fb080f6bc&c=moa&idno=ABA1561.0001.001&view=toc">here</a>.
  This book was published in 1856, and may be very helpful indeed for
family research.

This is the same comment as above, but cleaner.

There is a Skirbeck in Lincolnshire, England.  Frequently Lincolnshire
is abbreviated "Lincoln", but they are one in the same.

You can see a map of Skirbeck here: http://tinyurl.com/3oms8 

There is no "Shirbeck" town or city in the United Kingdom, and this is
most certainly one in the same town.

If your family is from this town, here are some pictures of churches
located there that may be of interest: http://www.bostonuk.com/gallery/neilwright/
 
The website also includes a detailed history of the area.

You can also do a full-text search of a History of Skirbeck and local
towns at the University of Michigan: http://tinyurl.com/67wfp 

This book was published in 1856, and may be very helpful indeed for family research.

Hi,
A good INGALLS resource is http://www.genealogybuff.com/data.htm#Ingalls

There are many genealogy tools out there that can provide a lot of
information in a very short amount of time.   I recommend
GenealogyBuff.com because upon submitting a surname, you can access
many of the "hidden" internet databases that exist to see what returns
you get.  There will be obituary archives, free vital records
databases, paid databases, birth records, death records, county
records, census records, etc.
There is also a library of files that have early and recent data
arranged by state and county.
Hope this helps in your effort.