Thanks. I know this is lame, but I don't know anything about computers.
Can a desktop PC Hewlett packard model p6710f run this game?

I do not think so.

I do not think that PC is DirectX 11 compliant. So it probably will not run at all.

Even if it does run, that PC is well below minimum specifications, so it would probably run painfully slowly.

No dedicated graphics card means you're going to struggle with most modern games.

On the good news front, you're definitely safe to play 70% of the Gog catalog and there are some pretty awesome turn based tactical games available. No other BattleTech themed ones, but enough to occupy you till 2022. :)