The wording of your question is somewhat unexpected, because generally we would assume a character would be admired first for his strengths, and we'd then ask if his weaknesses also would be admirable in a way. However, Hamlet's vulnerabilities and problems have come to be seen as so central to his character that you're correct in asking if his strengths, whatever they may be, come through as well in terms of our ability to relate to him.
The question is a good one because we have to ask if Hamlet really does have strengths in the normal sense of the word. He has courage, but one could counter that this stems from his being in such as state of depression that he doesn't care about his own life. Most of his behavior, I would argue, does not conform to the usual way in which we conceive of either "strength" or "weakness." His actions toward women--both Ophelia and his mother--are resentful, defensive, and abusive. In Ophelia's case he is apparently using her as a means of demonstrating to the King and to Polonius his feigned madness. This does show weakness on his part, but it is not the sort of vulnerable weakness with which one can empathize. Our empathy for Hamlet comes from the recognition of his suffering, of the severity of his disturbed mental state. The question boils down to whether or not there is a strong or at least decisive part of Hamlet's nature with which we can identify as deeply as we do with his depression and with the way he expresses the universal human "predicament," especially in the "To be or not to be" soliloquy.
As stated, Hamlet is fearless. At the same time there is a ruthless, defiant quality about him. We can identify with this almost in the way we do with Macbeth when, at the end, Macbeth defiantly straps on his armor and goes out to fight Macduff even though the more "honorable" thing would have been to commit suicide. At Ophelia's funeral, Hamlet reacts harshly and antagonistically to Laertes' grief over his sister:
Now pile your dust upon the quick and dead,
Till of this flat a mountain you have made,
T' o'ertop old Pelion or the skyish head
Of blue Olympus.
(comes forward) What is he whose grief
Bears such an emphasis, whose phrase of sorrow
Conjures the wandering stars, and makes them stand
Like wonder-wounded hearers? This is I,
Hamlet the Dane. (leaps into the grave)
One can say Hamlet's anger has been aroused by Laertes' also having said:
Oh, treble woe
Fall ten times treble on that cursèd head,
Whose wicked deed thy most ingenious sense
Deprived thee of!
But one would think that if Hamlet were a person with decent feelings himself, he would have acknowledged the correctness of what Laertes has said and would have expressed, or at least felt, some degree of regret. Instead, he goes on the attack. In some way, we as readers can sympathize with Hamlet's remorseless and untrammeled defiance, perhaps because we instinctively feel that Laertes and all the other courtiers are themselves false and venal. Hamlet is the only honest one among them, the only one who does not lie and who tells the truth even when he is pretending. That is one strength we can admire.