Some things not adding up
Your original post mentions the first address in the DHCP lease block is 192.168.2.150, but the PC is asking for .2.101. That is outside the block and may be the reason why the router is not responding.
Setting the router to .1.64 has no impact on the modem leasing out the address. It has no clue you assigned it to the router. (Some servers ping an address to be leased out of precaution, but not your modem apparently.)
The main thing is that the broadcast should not go through the router. In your case it does, so your "router" seems to be acting as a switch. If it is one of those 4+1 port thingies, are you sure you have the modem plugged in the "internet" port? If it really is a switch, then you'll have to make one of them stop acting as a DCHP server as the broadcasts will keep reaching both devices.
Lastly, what are the netmasks? Usually these devices use a 24 bit mask, but the modem seems to use at most a 23 bit mask. If it is even less, then the networks of the modem and router overlap which can lead to other problems. I usually switch one of the devices to a 172.16 network if they both are set for 192.168.x.x.
