You can use PostGIS to achieve what you need. PostGIS has a function called ST_line_interpolate_point(geom, location) which can take a line string e.g your road, and a location which is a percentage from the start of the road e.g distance/road_length.
I would, as I did this at work last week for something like this, create a table with your Accidents (events) and a table with your roads (just upload the one you have from QGIS into PostGIS using SPIT) and then join them using a common attribute.
SELECT ST_line_interpolate_point(roads.the_geom, event.distance / ST_Length(roads.the_geom)), event.id
FROM event
JOIN roads on event.roadid = roads."TIS_Code"
The above syntax might not be 100% but should get you some of the way. You might have to tweak it to handle if the road is shorter then the event distance etc (this might work added to your join WHERE event.distance > roads.BEGM AND event.distance < roads.ENDM)
If you want to then get the corrdinates from the points you can use the range of ST_As... functions or you can wrap the above query in a another query.
SELECT ST_X(point),ST_Y(point), id
FROM (
SELECT ST_line_interpolate_point(roads.the_geom, event.distance / ST_Length(roads.the_geom)) as point,
event.id as id
FROM event
JOIN roads on event.roadid = roads."TIS_Code")
Works like a charm.
EDIT:
This might work better:
SELECT ST_line_interpolate_point(roads.the_geom, event.distance / ST_Length(roads.the_geom)), event.id
FROM event
JOIN roads on event.roadid = roads."TIS_Code" AND event.distance > roads.BEGM AND event.distance < roads.END
Create a dynamic graticule (graticule.mbx)
To add a graticule to a map, select "Add Graticule"; to remove a graticule select "Remove Graticule". These commands can be found on the Graticule sub-menu on the Tools menu, or when you right-click on a map window. Note: you can only have 10 windows with graticules at any one time in any one MapInfo session. If this is a problem for you, remove the graticule from one of the windows, or re-compile the programme with a higher limit.
Once you have added a graticule to a window, the graticule will re-draw as you pan and zoom in and out, and as you change projection.
The graticule will usually be in the current coordinate system - e.g. with a New Zealand Map Grid projection you get an NZMG grid. However if the coordinate system is a non-degrees system (like NZMG, which is in metres) and you set map coordinate units to Degrees (in Map Options) you will get degree lines projected into the current system. This will usually give you some sort of interesting curvey lines for your "grid".*
http://mapinfotools.com/index.php?option=com_sobi2&sobi2Task=sobi2Details&catid=9&sobi2Id=398&Itemid=53
Best Answer
Natural Earth has these lines look for Geographic lines and Graticules under Physical (not my first guess). The data is free for all possible uses.