I tried the boards again. The NC-C386CT runs fine with jumper on the turbo connector (at 33 or 40MHz, depending on one jumper).
I removed the cache from the MS-3121 and set all jumpers below the cache to 2~3. This disabled the cache and board now boots without problems. Seems that the cache controller is bad. I put the cache to NC-C386CT (8 ATT chips) - there is no space for the 2 28-pin Toshibas (there are three 24-pin sockets with 2 22-pin Toshiba chips). The cache works fine.
I also tried the PC Chips M321 board with the cache - it runs OK too.
Here are some benchmark results (all boards with AMD Am386DX/DXL-33 CPU running at 40MHz - overclocked

, Trident TVGA8900C 1MB ISA SVGA card, ISA HDD controller and 40MB Maxtor drive) from CheckIt:
NC-C386CT, default BIOS settings, no cache:
5816 Dhrystones
117.4K Whetstones
13546 CPS (BIOS video)
67932 CPS (Direct video)
NC-C386CT, tuned BIOS settings, no cache:
6765 Dhrystones
141.7K Whetstones
16255 CPS (BIOS video)
80748 CPS (Direct video)
NC-C386CT, tuned BIOS settings, 64KB cache:
11631 Dhrystones
204.7K Whetstones
25273 CPS (BIOS video)
131378 CPS (Direct video)
MSI MS-3121, default BIOS settings, no cache:
4911 Dhrystones
102.9K Whetstones
11407 CPS (BIOS video)
57678 CPS (Direct video)
MSI MS-3121, tuned BIOS settings (used AMISETUP), no cache:
6765 Dhrystones
141.7K Whetstones
16255 CPS (BIOS video)
80109 CPS (Direct video)
PC Chips M321, no cache:
4804 Dhrystones
102.0K Whetstones
12504 CPS (BIOS video)
58319 CPS (Direct video)
PC Chips M321, 64KB cache:
11049 Dhrystones
213.2K Whetstones
25273 CPS (BIOS video)
132660 CPS (Direct video)