Answer: To grow a successful lawn, the area needs to be sunny all day or for at least half the day and the soil must be well prepared. Based on your description, it sounds like your front yard may just be too shady for lawn grasses. You might want to consider using a shade tolerant ground cover instead of grass. (This might also be easier than trying to mow a slope.)
In general, to establish a healthy lawn you would start by running some basic soil tests to check fertility and pH. Then you would fertilize and possibly also add lime based on the test results.
Regular mowing to the correct height can also help the lawn grow thick and crowd out weeds. Set the blade high at about three inches. Mow often enough that you never remove more than one third of the grass height at a time. This can mean mowing more than once a week.
If you fertilize and lime per the test results and mow correctly all season, you may see some improvement. If not, the best time to redo a lawn is actually late summer to early fall. Your local county extension should be able to help you with the soil testing and interpreting the results, and with developing a lawn plan.
In the meantime you may find some of their web publications helpful. You may need to cut and paste the complete url into your browser to make it work correctly.
Good luck with your lawn this summer!
Q&A Library Searching Tips