Do you really need all of the fields to get a count??
Maybe start with something simple and add fields as needed, checking to ensure the count doesn't change.
Code:
SELECT MPL.DBA, MPL.Mnemonic, Count(Providers.Mnemonic) AS CountOfMnemonic1
FROM Providers RIGHT JOIN MPL ON Providers.Mnemonic = MPL.Mnemonic
GROUP BY MPL.DBA, MPL.Mnemonic, Providers.[Active / Inactive]
HAVING (((Providers.[Active / Inactive])="Active"))
ORDER BY Count(Providers.Mnemonic);
<snip>but initially they just asked me to transfer the excel sheets to Access.<snip>
Have to say, the MPL table does look like it came from an Excel spreadsheet. 
It looks to me that the MPL table could be broken into at least 12 more tables.
Having linking fields that are text is not the most efficient method for linking tables. Should be Long Integers.....
Also.....
Object names should only be letters and numbers - NO spaces, punctuation or special characters (exception is the underscore).
You have spaces,
special characters ([Active / Inactive], [IMO Go-Live Date], [KVM Switch (Yes/No)]) and
punctuation ([Need ImmTrac Upgrade?]) in your field names.
My $0.02............
Windows 7 32bit 
Access 2007
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