I find the liturgical and rabbinic descriptions of the atonement process on Yom Kippur challenging. Without a Sanhedrin to mete out punishments for intentional sins, and no altar to bring offerings to atone for unintentional or un-witnessed sins, the chance of ever starting the year with a clean slate seems bleak. But we are also led to believe that sincere repentence wipes out all sins. Can we ever start with a truly clean slate? Or will we still be held liable for sins we don't get punished for in this world?
Repentance absolves all sins. However, depending on the nature of the sin, full atonement may be immediate or may be contingent on something else.
- Violation of a positive commandment (that does not carry karet) is forgiven immediately upon repentance. (1:9)
Violation of a negative commandment (that does not carry karet) is partially forgiven upon repentance, but only fully forgiven on Yom HaKippurim. (1:10)
Violation of capital offenses or offenses that carry the penalty of karet, are partially forgiven through repentance and Yom HaKippurim, and are fully forgiven through suffering. (1:11)
Violations that cause desecration of God's name are only fully forgiven upon death. (1:12). These are sins which are done to anger God (Hilkhot Yesodei HaTorah 5:13).
Interpersonal sins require restitution to the damaged party as well as his forgiveness. (Hilkhot Teshuvah 2:11)
So as far as positive and negative commandments, one will indeed start the year with a clean slate (provide that he repents). Even the more severe sins carrying the death penalty or karet do not require the Sanhedrin or the sacrificial service to achieve atonement.
In summary, no, not ALL sins.
There are several aspects to answering your question, and I couldn't get to all of them, here.
But to start, Talmud Yevamot (don't know exact page) explains that Yom Kippur never atones for sins between one person and another until that person requests forgiveness, personally. The method becomes a bit more complex if the wronged person is unreachable or dead.
Another more difficult example is atonement for lashon hara and rechilut (gossip, slander). How would you now how many people got the bard word about someone, and how could you really recover the damage already done?
Yet another concept is inferred from your mentioning that we don't have a Bet Hamikdash and we carry the sins of our ancestors. This concept is hinted to in a few places in our daily prayers (esp. Tachanun) and the fact that we still don't have a Bet Hamikdash is an indication that we have not yet been forgiven.
Finally, what about all those sins that we did during the year, but on Yom Kippur, we forgot about them and didn't mention them in our confession? We're still responsible.
The first perek of Shevuos, summarized in Rambam's first perek of Hilchos Teshuvah, says that certain sins are atoned for immediately by teshuvah, certain ones are atoned for by Yom Kippur, though Teshuvah delays the punishment in Olam HaBa, and certain sins are atoned for with suffering, though Teshuvah and Yom Kippur delay the ultimate punishment. Chillul Hashem is the harshest of all; its atonement comes only with death, and the above three delay the punishment until then.
Also, as discussed in the last Mishnah in Yoma, there's another requirement for sins between man and his friend, which is asking for forgiveness.
As the Rambam (ibid.) notes, none of these sources say anything about karbanos. To the contrary, our Teshuvah takes the place of the karbanos, and, as the Midrash (Vayikra Rabbah 7:2) points out, is even better than karbanos:
One who does Teshuvah is as if he went to Yerushalayim, built the Beis HaMikdash, built the Mizbeiach, and offered upon it all the karbanos in the Torah, as the passuk says, "The offerings of Hashem are a broken heart."
Emphasis mine: not just the applicable karbanos to the sin in question, but every last one of them.