Hi artistic.maze. Moog is using the sidereal zodiac, where as you and Zuri (and I and most astrologers) are using the tropical zodiac. That's not to say one is better than the other. I don't have any experience with the sidereal zodiac.
Whatever sidereal astrology can also say about your lack of affintity with Capricorn energy, tropical astrology, as Zuri has said, shows that it will be difficult for you to tune into your Capricorn Sun due to the prominence of fire (Sagittarius is a fire sign as you may know) in your chart. You could get a lot from reading up about Jung's functions of consciousness, perhaps in books like 'Relating' or 'Astrology for Lovers' (both by Jungian analyst and astrologer Liz Greene). Fire and earth are opposite elements, so you you will need to make conscious effort to express the Sun, which you must do to fully tap into your vitality and sense of worth.
Libra rising isn't incompatible with a Capricorn Sun - both these signs are concerned with acting in accord with some set of rules. Capricorn is more practical, while Libra is more idealistic, but they are both very aware of etiquette and social mores. Sagittarius is also socially aware, but in a different way. Sagittarius is on a quest to find meaning and inspiration and this quest could be undermined by the needs of Libra and Capricorn. Sagittarius needs to be broad minded in a way that is not in Libra 's and Capricorn's natures.
Libra and Sagittarius get on well - both are motivated by ideals of social integration. I would say that both the Capricorn and Sagittarius energies can be expressed very well through the Libra Ascendant, but that you will have to put effort into cultivating the expression of the Sun in Capricorn, especially as the Ascendant ruler (Venus - because it rules Libra) is in Sagittarius.
Looking at your chart, Jupiter (ruler of the Sagittarius planets) in Capricorn, and the strong aspects between Saturn and some of the Sagittarius planets, underlines the need to integrate Sagittarian and Capricorn energy. Also, Saturn is in the 9th house - the house which has affinity with Sagittarius.
You have a few angular planets, one of which is that Sun in Capricorn. The Sun is often associated with the experience of being fathered, as is the particular angle on which your Sun is placed. You might have seen him (assuming you knew him) as a Capricorn type. Whether he was a positive role model for this energy, or whether his way of expressing it grated with you and put you off expressing it yourself, is perhaps relevant to the hurdles you may face in trying to own that energy for yourself. It is important that people with Sun in the 4th house develop a sense of themselves as more than just a product of their family. Capricorn is about self-sufficiency - one possibility with this chart is that you still let your family be responsible for you in a way which prevents you from living out that Capricorn Sun for yourself. This is all speculation of course - you can decide for yourself what fits your actual experience.
The Sun in closely square the angular Chiron. Chiron in the 7th house suggests pain in early relationships which may affect adult relationships. The Sun Chiron square suggests a possibility of a father who for some reason was wounded by life, and that this affected his ability to inspire you with the confidence to truly enjoy being the person you uniquely are. This part of your chart is under the spotlight next year as transiting Uranus and Pluto move further into Aries and Capricorn respectively. This will be a time of dealing with any wounds or fears around that Sun Chiron square. Any disruption should be seen as potentially very productive in the long term.
The other angular planet is Pluto on the ascendant. Pluto is a watery planet, and probably therefore not the easiest planet for you to deal with because you have no planets in water signs. But the planet will obstruct your life path if not consciously embraced, as will any planet on anyone's ascendant. The last year or to may have seen life confront you with this issue, as transiting Uranus and Pluto made apsects to the ascendant and Pluto in your chart. Pluto on the ascendant is definitely something you should read up about to give you important information about your disposition and path to fulfilment that you won't get from looking at the sign placements in your chart.
Anyway - hope I haven't bombarded you with too much stuff or loads of stuff which doesn't apply to you.
Best wishes