TLDR; You will need to upgrade the Dell power supply in the 3670 to run a decent graphics cards, but you CAN find a power supply that will fit in the case and you CAN fit a current high end graphics card.
Now, here is my base build, ordered direct from Dell during a recent sale;
210-ANZR Inspiron 3670
370-AECJ 12GB, DDR4, 2666MHz
338-BNQJ 8th Generation IntelR Core i5-8400 processor (9MB Cache, up to 4.0 GHz)
321-BDIR APFC Chassis with 290W PSU (Silver front BZL)
400-AVNX Dual Storage (3.5' 1TB HDD+ M.2 128GB SSD)
490-BDMO Intel UHD Graphics 630 with shared graphics memory
Out of the box the system was able to play Fortnite at 60 fps with view distance at epic and all other options at their lowest setting. I use a PS4 controller paired via Bluetooth and the InputMapper app for gameplay control. With this setup, the onboard GPU was constantly at 100% and using all available memory. My objective was to boost this system so that I could play at 144 fps, with the same optional settings. My upgrade consisting of the following parts:
Power Supply (sourced from Amazon):
FSP 450W Mini ITX Solution/SFX 12V / Micro ATX 80 (FSP450-60GHS(85)-R1)
Eyeboot 24 Pin to 8-Pin Power Supply ATX PSU Adapter Cable for DELL Motherboards
Video Card (sourced used from Ebay):
EVGA GeForce GTX 1060 SC 6GB Overclocked
Install Notes... Despite many posts to the contrary, the PSU fit in the 3670 case with only very minor modification. You will need to first install the included PSU ATX adapter plate. All 4 mounting screws align perfectly between the adapter plate and the Dell case. Next install the PSU onto the adapter plate, it will require 3 screws installed in specific order. First, install the screw in the upper left hand corner, this will go in without any obstruction. Next, install the screw in the lower left hand corner, this screw is slightly obstructed by the case sheet metal, but will still go in without modification (when done in the order described). Finally, the third screw on the right hand side is completely obstructed by the case sheet metal. To get this screw to fit, drill a small hole in the sheet metal inline with the adapter plate screw. Be careful not to drill into the power supply, it does not take much force, with a good drill and bit, to make this hole. No need for a dremel or any major modification of the sheet metal and the simple hole does not create any structural problems with the case. Now you can secure the 3rd mounting screw on the right hand side and the power supply will be firmly installed in place, slightly suspended from the case bottom. The fan will face into the case, as required, no additional modification or re-orientation of the PSU is needed. Use the 24 pin to 8 pin adapter to make the motherboard power connection and then use the 4 pin cable to make the direct connection to the accessory power lead. That's it, just 2 cable connections.
With the PSU in place, next install the GPU into the PCI Express slot. This will require you to remove the two sheet metal plates for the PCIe slot and the slot immediately to the right of it. The GTX 1060 SC, which is a short length card, fits into the case and the FSP PSU provides the required 6 pin power cable needed for secondary power. I had to slightly bend the GPU bracket's lower tabs to get them to lock into position, otherwise no other modification required. Now boot the system back up and install the Nvidia 10 series drivers for Windows 64 bit. You should now be able to use both the onboard GPU and GTX GPU outputs. Making sure you have the GTX GPU outputs connected, reboot one final time, go into BIOS setup and set the GTX GPU as the primary adapter.
Conclusion... No need for an external power supply or for an older low performance video card to turn the 3670 into a decent gaming rig. I'm up and running with Fortnite at 144fps and difference in aiming is pretty significant. Total cost for the build was around $735, with the 3670 ordered direct from Dell, the PSU and adapter new from amazon and the GTX 1060 SC used from ebay. In comparison, a similar system from Costco with a inferior PSU and video card is over $800.