Cant purchase third party games on Xbox

By third party games, if you mean from places other than the Microsoft Store, then yes, you can't purchase from them

If you mean games not made by Microsoft but officially released on the Microsoft/Xbox stores that would be extraordinarily unusual and you'll need to give a lot of details please

was the game purchased by a third party or on xbox?

if purchased by a third party there is nothing that can be done from Xbox side of things.

if you purchased via Xbox and you have been charged you should find the game already in your my games & apps. ready to install.

if you purchased a code and should receive an email from a third party source be sure to check your junk mail and or spam folders to make sure its not got lost, if still nothing contact the seller.

Was the hard drive purchased brand new or was it purchased used/from a third party company like ebay? If it was purchased used/from a third party, it's highly likely to be a knock off no matter how official it looks. So it may not have the emulation software
required to play original Xbox games.

Purchasing games from unauthorized third-party retailers is not supported.

Was the hard drive purchased brand new from a retailer or was it purchased use or from a third party company like ebay? If it was bought used or from a third party it's possible the hard drive is a knock-off which would not run original games.