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If you haven't already done so, try unplugging the DVR and plugging it back in again. Like a crashed PC, once it locks up, the only way to make it responsive again is to restart it. Generally most PVRs carry out a check disk operation if they didn't turn off properly, so this will unlikely affect other recordings.
If the unit refuses to start up or this program refuses to delete even after turn off/on the DVR, then there is likely a file system corruption on its hard disk. In this case, you will likely need to format (erase) its hard disk or contact DirectTV about the issue.