Using GDAL command line to copy projections
I would recommend to use gdalcopyproj.py, a sample file from the GDAL repository done for this purpose as mentioned directly in the script:
Duplicate the geotransform and projection metadata from one raster dataset to another, which can be useful after performing image manipulations with other software that ignores or discards georeferencing metadata.
The command line is just:
gdalcopyproj.py source_file dest_file
Use gdalsrsinfo to get the srs of the tiff that still has the projection:
gdalsrsinfo -o wkt tiffwithsrs.tiff
Then copy the output and use gdal_translate to apply it to a new tiff:
gdal_translate -a_srs '...' tiffwithoutsrs.tif newfixedtif.tif
just paste your projection after the -a_srs option
I would use listgeo http://www.remotesensing.org/geotiff/listgeo.html and then geotifcp.