Hi Tom Welcome to the forum.
The Rom loaded on your vega is probably just corrupt so it should be no biggie.
You mention the advent splash so you are using a stock rom but it is helpful if you mention what Rom/version you are using (If you dont know this can also be useful to know).
You will need to flash a new rom to your vega to correct the problem.
The back/power button thing will put the tablet into NVflash mode so you can flash a rom using a PC and a USB cable. There are several stumbling blocks that may be causing your problem to get past first.
First thing (probably what you are doing wrong), the vega needs to be powered off completely before doing the power/back button thing. To do this press the power button to turn on the vega so the screen lights up and it starts to boot, now press and hold the button for 12 seconds (may not need to be that long but you cant press it for too long). You are now properly off and can hold the back button down for 2 seconds, then while still holding the back button press the power button for 2 seconds and then release the power button followed by the back button. If the screen lights up you have done it wrong, try again. When in NVflash mode the tablet looks like its off but you will hear a ping from you PC (if the usb cable is plugged in) and a notification on the task bar (windows) that a new device has been found. If you already have the driver and it installs automatically you will be able to flash a rom now but if the driver is missing windows should let you know (in the notification area or a popup when the device is detected). If you dont have the driver do a search on here for Audi (automatic usb driver installer) or Vegatools (includes Audi) they will assist you in installing the usb driver and vegatools is a really useful tool to have (helps flashing roms too).
If you have tried all of the above and you still cant get a PC to detect the vega then check the USB cable is the undamaged and is USB 2.0 as some people have had trouble with old usb 1.0 cables.
Good luck
P.S. as you are flashing a rom you may want to flash a custom rom. Try corvus5 SP1 for stability and smoothness (Andriod 2.2 froyo) or if you are a bit more adventurous and want more up to date features try Vegacream (Android 4.0.1 IceCreamSandwich) or Honeyice (Android 3.1 Honeycomb). The improvements in any of these roms will be a big surprise after just using the stock rom.
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