It is a good question.

And, in fact, there may be a need to discuss about this among the ETSAP partners.

As it is now, there are some inconsistencies between the documentation and the TIMES code in this matter.  In the TIMES code, it is always assumed that if no hurdle rate (NCAP_DRATE) is specified, the present value of the annualized investment payments at the beginning of the commissioning year should be equal to the original lump-sum investment cost (plus any interest during construction, if NCAP_ILED is specified). In other words, the annualized investment costs included in the objective function are equivalent to a single lump-sum payment INV that would occur at the beginning of the commissioning year.

In the same way, if a hurdle rate (NCAP_DRATE) is specified,  the annualized investment costs included in the objective function are equivalent to a lump-sum cost INV_S that would occur at the beginning of the commissioning year, where   INV_S  = INV * CRF_S / CRF, as explained on page 163 of the Documentation, Part II.  As stated there, the correction factor  CRF_S / CRF  is used to multiply every investment cost (and salvage value), according to the difference between G_DRATE and the hurdle rate, when specified.

See: http://www.iea-etsap.org/docs/TIMESDoc-Details.pdf

However, there is some inconsistency between the cost accounting in the objective function and the annual cost reporting: When the investment costs are reported, they are always annualized by using the standard CRF formula (as given on page 140 in the doc).

I hope the explanation above makes sense!

Ahh... I realize that my explanation didn't answer to the first part of your question.

But that part should be clear already from the documentation:

General discount factor for year y:    r(y)=1/(1+d(y)) 

Present value factor for costs occurring in year y, discounted to the beginning of year z: 

DISC(y,z) =∏_{u=z to y-1} r(u)

Therefore, you can immediately see the answer to your question "Is an investment made in 2040 discounted for 10 years by 3% and then by 4% until the baseyear or is the discount rate of 3% used for the entire timespan to the baseyear?” The answer is, of course, that the present value factor DISC(y,z) for e.g. costs occurring in y=2040 does indeed include the impact of the 3% rate for 10 (or 9) years, and the impact of the 4% rate for all the preceding years. 

And the answer to your  final question should be equally clear: the  present value factor DISC(2035,z) for investment payments occurring in year 2035 does include the impact of the 3% rate for several years.