The problem is not that you have a trial version of InDesign, it can happen also with a full version. After you have exported your file to png or jpeg, open it in Photoshop, resave it and all should be OK. Better : export it to PDF, open it in Photoshop and save it in jpeg or png directly with Photoshop.
If you export to PDF, export as PDF/X-4 and work always with RGB images, what always should be the case.
Even better still - create your letterhead in Indesign :-)