The good news is your Jasmine is still alive so it survived the winter. The bad news is that part of the vines have died back and turned brown most likely because this tropical plant hates the winter. You can start fresh by pruning your vine to within one foot of the soil for a fresh start. Grow in a warm spot with as much sun as possible for the most blooms. Give moderate to regular watering, fertilize with Osmocote every spring for continuous nutrients released slowly as the plant wakes up and starts to grow. It is best if tender plants like your Jasmine stay dormant during cold weather so water very little while it is in the greenhouse. Then each spring you can cut back the vines just before new growth begins in March or April.  You may have to wait until mid summer for the vine to flower each year but the sweet fragrance will be worth the wait. Keep growing, Marianne Binetti