Placing PNG file without losing quality. Comes out pixelated.

When you place an image file into Illustrator, the Control panel will tell you how many pixels per inch (ppi) the image has. If the number is low (large pixels), it will be "pixelated". If the number is large, it means the pixels are smaller, and it takes more to fill an inch.

If you drag the image, you scale it, and this changes the effective ppi. Here is the Control panel for the same image:

• First scaled smaller with the Shift key
  
  
  
• Second scaled larger with the Shift key
  

• Third scaled and distorted without the Shift key
  

Clicking to place will place the image at 100%. Dragging while placing will scale the image. Best practice: click, don't drag, when placing.

Also:

Be sure you are viewing the image at 100%. It will appear pixelated if you are zoomed in, but that does not have any effect on the printing.

I would try opening each file in Photoshop to confirm that the files are indeed pixilated.

The problem is with the quality of the original jpeg and png files, not with Illustrator. Both jpeg and png can loose quality when scaled. You need vector artwork from the company.