Hi Baron- yes it's sometimes possible to check semis in circuit but to be absolutely, positively sure it's best to unsolder them and bench test.
I suspect however, that the OP's board has some other problem though- SCRs are pretty hard to kill...
M
ps looks like TYN412 is the part number- 12 amp, 400 volt devices- they do match the drawing I posted- If you need to buy replacements Littelfuse S6020L or S8020L would be a good substitute with more voltage and current capability