Thank you!  I'm hoping that the power cable will work (can't see why it shouldn't).  I may have one more go at Fry's to see if I can find it there.  I do appreciate your response.  My more helpful than my googling had been.

I had downloaded the pdf of the service manual but it's really not very good and, in my opinion, they should have put one in the box with the tower.  Sadly it doesn't say anything about the types of cables etc, but does tell you how to remove and replace things like hard drives.

Thank you again for your help!

I do not own a 3670  however

http://topics-cdn.dell.com/pdf/inspiron-3670-desktop_service-manual_en-us.pdf

SATA Power Cable for Dell Inspiron 3653 3650 3655  GP2JM

https://www.amazon.com/Eathtek-Dell-Inspiron-3653-3650/dp/B06WP4KMQB

Dell VOSTRO/Inspiron 3669 3668 3667 3660 3650 3653 3650 3268 3250 , Compatible Dell PN GP2JM for X9FV3 caddy

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@Shadowmichael wrote:

 an old 3.5 hard drive from my old computer (with all my pictures etc on the old drive) 

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IMO, a 3.5inch spinning HDD, used in this capacity (as a data drive ... moved from one PC to another) works better as an external. I would have just bought this (or similar). They will have them at Fry's also.

USB-3.0 External 3.5inch HDD Enclosure ( with UASP Support)

But watch costs ... if HDD is small and old (ready to die), well new Seagate or WDC externals are pretty cheap.

Dell sales support could not help me. The fellow did not know what I needed and just sent me a couple of pictures that were not correct. I must have been on the phone for 30 minutes. There are no cable part numbers in the service manual. The inside of the 3670 is unlike any other PC I have worked on. First, you can't put two 3.5" drives in it and second, the power supply does not have three or four extra SATA power cables coming out of it. The proper cable has a 6 pin connector (2x3) that plugs into the MB and a RIGHT ANGLE power connector for the HD. A typical daisy chain power cable will not work because the two drives are not stacked so the spacing between the HD plug ends has to be 6-8". Please help me. I have found nothing on ebay.

To be perfectly frank and honest, I took the computer back to Best Buy where I had bought it and got a return then bought an HP.  I was told that the power cable was a "proprietary" cable by two different stores and that was enough to me off.  I was not willing to wait and see if I could order the cable, nor was I willing to waste any more time dealing with that machine. I think it's ridiculous that Dell would build a machine where you can't just slap in a drive easily.  Pretty sure they have lost me as a customer.

The 3670 power supply has NO SATA power connectors.  Those come from the motherboard.

I posted Links to the cables on Amazon not Dell Support.

I found something locally that works:

http://www.microcenter.com/product/318702/6-sata-15-pin-power-y-splitter-cable

The two female connectors are right-angle. Straight connectors (for both power and data) will not work because the PC cover does have enough space. 

I looked at the service manuals for all three Dell chassis styles; 3650, 3670 and XPS. They are all a mish-mash of unique motherboards, cables, power supplies, hinged fold out sub-chassis', etc. This 3670 was for my grandson. My five year old XPS 8700 is wonderful to work on. I have two 4TB 3.5" RAID 1 drives, and an M4 eSATA boot drive. I will upgrade from my i5 to and i7 and live with it for another 3 or 4 years.

While this cables posted elsewhere in this thread may be made to work, they are not actually the correct cables.

The Inspiron 3670 existing SATA Power Cable with one SATA power connector and one CD-ROM power connector that connects to the motherboard via a small 6 pin connector is Dell Part #:  05TK4F

I believe this part number is the same for the Vostro 3670 because the motherboards seem to be almost identical between the Vostro 3670 and Inspiron 3670  (except the Vostro 3670 has a PCI slot where the Inspiron 3670 has a spot for the PCI slot but no actual PCI socket).

Does anyone know the actual part number for the 2nd SATA power cable for the Inspiron or.Vostro 3670?  Hopefully one with two SATA right angle reverse power connectors and a single 6 pin connector for the motherboard.

Ouch, we could have easily gotten you on the right track with a little patience.

The aftermarket cable I suggested above worked fine. The two "outputs" are right angle in the correct orientation. You just connect it to the end of the existing power cable and connect the two outputs to the two drives. The existing power cable with the separate CD power plug will still be connected. Forget about the "original" Dell cable.

I found the part number on the little tag and e-mailed it back to the customer service rep I originally talked to. He never responded anyway.

Forget about the "original" Dell cable.,,,,,

I should have said forget about trying to hunt down a second OEM cable.

Does anyone have pictures of it installed? I want to see one with a sata power splitter installed.

The problem I have is the splitter I bought is the wrong orientation. And due to limited space it can only go in a certain way. I need help with pictures included 

You always need to make sure if you need 90* ends or straight ends when you buy cables.

Hey I need the 90 connectors because the case has very limited space. I ordered some but the little notch is on the wrong side. I need some with the notch on the right side when the connector is facing down and forward. I can send you a picture of the SSD orientation to you can see how it’s getting installed.

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@Duro1990 wrote:

 but the little notch is on the wrong side. I need some with the notch on the right side when the connector is facing down and forward.

AFAIK, there is only one kind a SATA cable. Either flip the drive or the cable (it could run down, around, and then up).