Any way you go, there is some work to be done and restores might not work ... depends upon what's in the 1.9 backups.
ConversionThingy ... may not be free to you ... besides, think this thingy is PC only and I don't own a PC and really don't want to spend a dime. ;)
http://www.conversionthingy.net/
Should note that above shows backups with no users. So is bringing users over to the 2 also important?
Other ways involve work.
Suggest taking ONE of the 1.9 backups and unzipping to a test folder to see what's in them. Since these come from another server you did not manage, who knows what's in them.
After extraction of the 1.9 backup zip to a test folder, look to see if there is a moodle.xml file at the root of that test folder. Open with text file ... should give specific information as to that backup.
1.9.x to 2.x is an 'adventure' PERIOD! Wish it wasn't, but there are many cirsumstances and variables invovled. Not sure anyone has done a site migration from 1.9.x to 2.4. Not sure it's even possible. Migration so far has been up one, test, up two, test, etc.
If you'd like another set of eyes on one of those 1.9 backups, go to:
acquire an account. Drop a line after you do to ktask@sosoftexas.org.
I'll escalate your access levels to a category and we can then both see the zips and how a restore of those goes in a 1.9.
Next step would be to test there and make sure things work. Then backup again. Have another 2.3 and a 2.4 sandbox we could try to restore to at that point. If successful, backup from the 2.x sandboxes and you should have something in .mbz to restore.
'spirit of sharing', Ken