How do I solve this graph with Dijkstra's Algorithm?
Firstly, I suggest that you start off with a simple graph (5 nodes would do). I believe you are mixing Dijkstra with A* search algorithm and are trying to perform A* search (even without knowing it).

For Dijkstra:


Assign to each node a distance value. 0 for initial node and infinity for all other nodes (since they are not visited)
Set initial node as current. Mark other nodes as unvisited. Create a set of all unvisited nodes.
For the current node, consider all of its neighbors and calculate their tentative distances. Compare the newly calculated tentative distance to the current assigned value and assign the smaller one. For example, if the current node A is marked with a distance of 6, and the edge connecting it with a neighbor B has length 2, then the distance to B (through A) will be 6 + 2 = 8. If B was previously marked with a distance greater than 8 then change it to 8. Otherwise, keep the current value.
When we are done considering all of the neighbors of the current
node, mark the current node as visited and remove it from the
unvisited set. A visited node will never be checked again.
If the destination node has been marked visited (when planning a route between two specific nodes) or if the smallest tentative distance among the nodes in the unvisited set is infinity, then the algorithm has finished.
Otherwise, select the unvisited node that is marked with the
smallest tentative distance, set it as the new "current node", and
go back to step 3.


If you need more help on this method, let me know!