Hi,
>
> When pdflatex converts *.eps files to pdf I get errors that these figures
> can't be converted and are not shown in the final pdf.  When  .ps files get
> converted, their boundingboxes are ignored so figures are not displayed
> properly.

This is a sign of corrupted eps files.
Missing bounding boxes can be restored by program called "ps2eps", 
http://www.tm.uka.de/~bless/ps2eps

After correcting your eps, you can try to push them through epstopdf again.

Hope this helps, 
Vasek

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