Our company had a number of issues when we deployed the e6400 with MEE 5.1.6 (I think that was build 5400 or 5420 or some such thing).
First, make sure that your machine group in the Admin Console is not configured to "Force USB." That option needs to be "unchecked" prior to installation on the e6400, and included in the install set in that "unchecked" state. Before we un-checked that option, our machines would get stuck in endless boot loop.
Second, make sure that your e-series machine is configured in BIOS to run in SATA / ATA mode rather than IRRT. MEE did not support IRRT (in my experience) until later revisions (5.1.7?). Leaving IRRT enabled caused our machines to get stuck at the "Starting SafeBoot" screen until we changed the drive mode (as soon as we changed drive mode in BIOS, the machine started successfully).
Third, I understand that some people have needed to enable the "detect number of OS sides" option in MEE as well. We have not, but might be worth a mention.