Remove the rosette off of the spindle.
Thru spindle too short on door handle.
One knob is fixed permanently to the spindle by means of a grub screw through the neck of the knob.
It seems the original had broken so it actually was too short to fit where it belonged.
Unscrew one handle and remove the spindle.
Once door is open remove old latch and replace.
Take old latch with you as there are numerous different sizes.
Remove the set screw securing the doorknob to the spindle then unscrew the door knob off of the spindle.
If that does not work try and use a thin scraper or similar to disengage the latch from the gap between door and frame.
Push on the handle until it fits against the corresponding trim plate at that side of.
Remove the knob and rosette from the other side of.
Hold the knob in one hand and insert the other end of the spindle into the square port inside the door lock.
The other end of the spindle and opposite knob is threaded so that this knob can screw on to the spindle and subsequently adjust for door thickness.
Try and use a big flat screw driver to open the door where the spindle use to go.
Mount the handle near the end of the the spindle on the spindle opposite the one that contains the larger flat ie.