Help with a logo.

Why not use the artwork from the original artist?  What about the original "Layered" Ps file which would allow you to ( hopefully ) delete the background or keep it a transparent .psd file?  The bitmap artwork may look good on your monitor several sizes larger than it will appear on your business card as reflective artwork, but you should avoid complex bitmap artwork for such items as business cards, and/or stationery.  3D artwork is meant for special applications, but is limited to its use.  I recommend you reduce the supplied artwork to the size you intend for the business card and get a proof made.  You might be surprised.  Stationery, signage, vehicle graphics, etc., all should be simplified to maximum 3 spot colors. 

Might be less trouble not to bother- the cheapskate client used that silly site, and then it looks like had issues with the designer..

Anyway, to try  maybe look at using some other software, eg Photoshop

https://design.tutsplus.com/articles/the-comprehensive-guide-to-bevel-and-emboss--psd-17308

That's a pretty extensive lesson to have answer on a forum, but to start, you'd use the .ai file. Under Effect, select 3D>Extrude and Bevel. This item uses a pretty low-looking extrude depth. And, you'll want to change the rotation settings on the top of the window to say "Front". Try setting the extrude depth to about 5pt with a classic bevel and maybe a 2pt height? Then, select More Options - and you'll see an area to affect the angle, brightness, size and more of the light source.

Hopefully, that'll give you a start...