Will the original Diablo/Hellfire and Diablo II/Lord of Destruction run on up to date equipment? Here is my rig.

CASE Thermaltake Level 20 GT RGB Plus Tempered Glass eATX full tower computer Case - Black
PSU Corsair AX 1600
MOTHERBOARD ASUS ROG Maximus XI Extreme 
CPU Intel Core i9-9900K
CPU COOLER NZXT Kraken X72 360mm 
RAM G.SKILL Trident Z Royal Series 32GB (2 x 16GB) 288-Pin RGB DDR4 SDRAM DDR4 3200 (PC4 25600) Desktop Memory Model F4-3200C14D-32GTRS
NVMe drives Samsung 970 EVO 2TB - NVMe PCIe M.2 2280 SSD (MZ-V7E2T0BW), Black/Red x 4
SSD Samsung - 860 Evo 4 TB 2.5" Solid State Drive X 4
VIDEO ASUS ROG Strix GeForce RTX 2080 Ti Overclocked Triple Fan 11GB GDDR6 PCIe Video Card
MONITOR Acer Predator Gaming XB273K 

Nice machine!

Sure it should run. GOG says so for the first game and I say it should for the second as you can always wrap it with something like dgvoodoo.

https://www.pcgamingwiki.com/wiki/Diablo_II

Remember the games were made for a much lower resolution so I suggest playing in a large window.

https://github.com/diasurgical/devilutionX
This is modern build of diablo 1

As for diablo 2, it runs for me without any problems

Diablo 1 was released before 64-bit Windows was available to the consumer market. It can't use more than 4G RAM, and it runs fine with much less than that. Diablo 2 was more resource intensive, but still should be fine on a much less capable machine than the one OP described.

just a joke :)