SCCM Task Sequence Installs Failing

I have strung together a Task Sequence for Operating System Deployment in SCCM. The OS, drivers and the first several applications in the TS install fine (Windows 7, Office 2010, Adobe Reader X, etc...) But when I get to Adobe Flash Player, QuickTime and a few others, these apps fail constantly during the TS installation. The strange part is that these apps install perfectly fine when I install them through Run Advertised Programs manually.

The only difference between the Run Advertised Program install and the TS install is that I am creating a separate program that does two things differently: for the Task Sequence install, I am unchecking "Allow Users to Interact with this program" (I have found that checking this box is the only way to get the program to install and allow the user to view progress, so this is how I have my non-mandatory assignments set. But this fails during the TS install so I have it unchecked for the TS). And I also have the option to "Allow this application to install through the Task Sequence without it being advertised" for the TS installation program.

But I continue to get errors like this one below. I stripped out the domain name in the message, but everything else is verbatim.

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The task sequence execution engine failed executing the action (Adobe Flash Player 10.2.152.32) in the group (Install Software) with the error code 2147516435
Action output: 16",PRG_ProgramID="Task Sequence Install",PKG_PackageID="CEN00058"'
Verified policy is compiled in 'root\ccm\policy\machine' namespace
content location count = 1
Invoking Execution Manager to install software
FALSE, HRESULT=80008013 (e:\nts_sms_fre\sms\client\osdeployment\installsoftware\installsoftware.cpp,282)
0, HRESULT=80008013 (e:\nts_sms_fre\sms\client\osdeployment\installsoftware\installsoftware.cpp,746)
Entering ReleaseSource() for \\NY446.domain.com\SMSPKGF$\CEN00058reference count1 for the source \\NY446.domain.com\SMSPKGF$\CEN00058\ before releasing
Released the resolved source \\NY446.domain.com\SMSPKGF$\CEN00058pInstall->Install(sPackageID, sProgramName), HRESULT=80008013 (e:\nts_sms_fre\sms\client\osdeployment\installsoftware\main.cpp,374)
Failed to invoke Execution Manager to Install Software for PackageID='CEN00058' ProgramID='Task Sequence Install' AdvertID='CEN20016' hr=0x80008013
InstallSoftware failed, hr=0x80008013
Install Software failed, hr=0x80008013.
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Everything posted on these error messages I have tried to no avail. Does anyone have any other suggestions, areas I could look? Again, I make sure I can install all of these apps through Run Advertised Programs before I create a new Task Sequence Install program for them. But they're failing during the Task Sequence install only and I can't figure out why?

The specifics of the error point to a failed dependency. I do have a chain of programs for the TS Flash install, but I have checked and doublechecked the dependency order and it is correct. What else would Flash be dependent on to install? Both IE8 and Firefox are installed in the TS before Flash.

E_FAIL_DEPENDENCY_NOT_RUN 0x80008013
 This program cannot run because it depends on another program that has not run successfully before. This error code is returned to task sequence manager when a task sequence Install Software Action step cannot be run because the step has a child program which has not been run before.