New motherboard and CPU. Is it worth it?

Well, if the USB and PCI-E slot are broken/not working, the upgrade makes sense. Where or what slot is your GTX 780 plugged into if the PCI-E slot isn't working? The top PCI-E slot on that board is the X16 slot; The others are either x8, x4 or x1, depending upon the boards brand name. Putting your new 780 in one of those slots might seriously bottleneck it.

You will have to upgrade both if you want to use that mobo or that CPU; your old CPU won't fit in the new board, nor will the new CPU fit in your old board. How long have you had that board? It has a 3 year warranty from ASUS. I had one of theirs go bad at 2yrs 10 months and they honored the warranty. (I had proof of purchase date and data).

No. No 32X. Your primary slot (blue) on your board is X16, and only that slot. On the new MSI board only the top slot is going to be x16. Two cards in SLI (slot 1 & 2) will run at X8. I think the days of two slots running at X16 are over; and there isn't much difference when two cards are running at X8 compared to two @X16.
Your current set up is quite good, even if the CPU is a bit dated. But I don't like having broken parts on a running system and I am sure you don't either. That is what makes this upgrade a decent choice.
Might want to do some research re. your psu, also. I have not been impressed over the years by Chieftec PSU's, but some of their units are made by Delta. Delta is a pretty decent manufacture. If you post a picture of the side label on the psu, or type it in a reply, we may be able to tell you how good (or bad) it is: Post the power specs, and especially the Underwriters number. This is found under an icon on the label that appears as a reversed R attached to a U.

O.K. first things first, and this is probably my last post for the night.
Below you will find a link to ASUS with the specs for your original mobo. Yes, both slots are called X16, but that black slot only runs at X1 by default, and I believe can be set to run at X4 in BIOS or runs automatically at X4 when you have an X16 card in there.
Basically, if it is broken, you aren't missing much unless you wanted to run SLI, then everything would run at x4. Waaayy below the speed of the 780.
https://www.asus.com/Motherboards/P8P67/#specifications

Thanks for the picture. Using the UL file code I confirmed that your psu is made by SIRFA, which is another name used by the manufacture Sirtec. They make some o.k. power supplies, but I would not run one in my system for fear of sudden catastrophic failure with accompanying destruction of hardware. Regardless of 80+ sticker it probably is not very efficient and I would be surprised if it could produce full power under any conditions let alone at an ambient temp of 40-50 degrees Celsius.
Your new system should get by just fine on a quality 600 - 750 watt psu - and 750 watts will be overkill. Power supply is the most important part of your system and usually gets no glory and people try to save money when they buy one: Remember, you have or will spend good money for this upgrade and should the PSU die it can destroy much of it.
Here are a couple suggestions:
SeaSonic S12II 620 Bronze 620W ATX12V V2.3 / EPS 12V V2.91 80 PLUS BRONZE Certified Active PFC Power Supply
http://www.newegg.com/Product/Product.aspx?Item=N82E16817151096
Rosewill CAPSTONE-650 650W Continuous @ 50°C, Intel Haswell Ready, 80 PLUS GOLD, ATX12V v2.31 & EPS12V v2.92, SLI/CrossFire Ready, Active PFC Power Supply
http://www.newegg.com/Product/Product.aspx?Item=N82E16817182071
CORSAIR TX Series CMPSU-650TX 650W ATX12V / EPS12V SLI Ready CrossFire Ready 80 PLUS BRONZE Certified Active PFC Compatible with Core i7 Power Supply & New 4th Gen CPU Certified Haswell Ready
http://www.newegg.com/Product/Product.aspx?Item=N82E16817139005
Seasonic is the best price here, all three are quality products by reputable manufactures: The CAPSTONE is made by Super Flower, the Corsair by Channel Well.
Other good brands/manufactures are XFX (made by Seasonic), Corsair HX 650 (Seasonic), EVGA V series (SuperFlower), Antec.

To end, I will reiterate my original answer: This is a good upgrade, all your parts will work with the new mobo and CPU, and your performance will increase; but you might want to consider a PSU upgrade also.

Heres the link to Underwriters Lab. cert. file;
http://database.ul.com/cgi-bin/XYV/template/LISEXT/1FRAME/showpage.html?name=QQGQ2.E320351&ccnshorttitle=Power+Supplies,+Information+Technology+Equipment+Including+Electrical+Business+Equipment+-+Component&objid=1079635430&cfgid=1073741824&version=versionless&parent_id=1073787374&sequence=1
Hope all this has helped.

To answer your questions in order fantomet: No, not much, and no.

Upgrading from a 2500k on a gaming pc is a total waste of your money. Unless you have $300 to throw at a 10% improvement. And even 10% is optimistic.

PSU recommendation I like.

Your PSU and it is an ok model. Definitely not as good as the top tier stuff, but I don't think it will blow your system up either.

That said, I would replace the PSU long before I would consider the 4670K. Not worth it coming from the 2500k.

I missed the part about the pci and USB slots being non-functional. If that presents a practical problem, then it does change the equation somewhat. But you could also just change out the board. Depends how how much money you have to blow.

thanks Fantomat. Let us know how the new parts work, and enjoy the season.