According to the XDA developer site, it's possible to get into the Axim's Diagnostic Mode by Presssing: RECORD + POWER + RESET. If you can get to the diagnostic screen, you may be able to reanimate your Axim.
Here's the link(s) to the discussion:.
Dell Axim X50v WM6 A01 (MagLite Edition) - Page 124 - xda-developers
Dell Axim X50v WM6 A01 (MagLite Edition) - Page 133 - xda-developers