
<PAGE>
 
                                                                    Exhibit 23.4

INDEPENDENT AUDITORS' CONSENT

We consent to the use in this Amendment No. 2 to Registration Statement No. 
333-9963 of Pierce Leahy Corp. of our report dated March 26, 1996, except for 
Notes 4 and 9, as to which the dates are June 13, 1996 and October 4, 1996, 
respectively, on the financial statements of InTrust, Inc. as of December 31, 
1995 and for the year then ended, appearing in the Prospectus, which is part of 
such Registration Statement, and to the reference to us under the heading 
"Experts" in such Prospectus.



DELOITTE & TOUCHE LLP

Denver, Colorado
October 22, 1996

