To change your visa from Business to work, either your present sponsor (who provided you the business visa) must provide an NOC to your employer (who recruited you) or you have to exit the country to issue a new visa to Qatar. These days business visa providers doesn't encourage to provide NOC because many companies have been blacklisted in recent times. Even if you are getting NOC, they will be charging you around the same amount you paid for renewal. Other best option is just exiting the country. Once you exit the country, your company can easily provide you a work visa within few days (if your company apply your visa online, then you can expect the visa before you land back to home). But some employers fools the people later they exit the country (rare cases), it happens when they find some one else better than the selected candidate/ company faces some issues (losing projects etc.). In your case, your company might be saying about NOC from previous employer. As you have never been worked in Qatar for the last two years, it is right. Regarding business visit, your present employer will be charged by Govt, a huge amount for each exceeded days after your expiry of business visa. You must talk to your company staff about this concern in detail. and please don't update your Fb status only after you get your first salary!!
By the way congratulations to your new job !! :)