Alinco DR-135T is, for those who can offer advice, a 10m (28MHz) all-mode transceiver - note to OP, such information is critical to the forum as not everyone is aware of what 'xyz-123' is without having to Google it..... pictures or links to websites really help.
Either way - Have you had a look through the user manual for any notes on indications of fault status?
This is a complicated piece of equipment as far as attempting repairs are concerned. If you are unfamiliar with test equipment and its use then unless the fault is 'user error' (i.e. a finger fault) then the process for identifying any internal failure and the subsequent repair of it may well be outside the remit of this forum and you may need ot seek professional help.
Is the device under any form of warranty?
Have you tried powering it up without the handset plugged in? A faulty handset could cause the fault you mention. If the set powers up OK without the handset then it's probable that there is a broken wire in the plug somewhere.