Then I get the message
Sending BOOTP Request
Then I get the error "no response or can't find IP"

Well, do you have anything that acknowledges BOOTP?  If you're just plugging the Amiga straight into the cable modem, the answer to that question is likely "No."  Hence your error.  Your Amiga is asking for an IP address by BOOTP, the cablemodem doesn't acknowledge BOOTP, and then the Amiga says "Duh, I don't have an IP address" and quits.

Try turning off BOOTP and jotting down the IP address, Subnet Mask and DNS server information obtained on your PC, and type those in as a fixed IP on the Amiga.  

Also make sure you power off your cable modem when switching between the PC and Amiga, as most cable modems lock to the MAC address of a single network card, and won't talk to any others until you reset the device.

I have a router stuffed between the cable box so one line goes to my PC, the other to the Amiga. I believe it is a dynamic IP address system which changes ?

Oh, well that's different then.  NARF!

Ok, the router probably does hand out dynamic IP addresses.  But it probably does this by DHCP, not BOOTP.  So your Amiga still isn't talking to anything that can give it an IP address dynamically.

I bypassed the BOOTP and entered the information. It allowed me to complete the installation wizard and when I ran the program it <> it was on-line but still was not connecting to the web when I stared AWeb II.

Well, it may have something to do with a bad DNS entry, bad default gateway, or more likely, this problem you mention below.

BTW - when I came back to my PC and looked at the screen it had popped up an error message stating that another computer on the system was accessing the IP address and that the connection from the PC might become unstable.

Yeah, I was assuming that the PC wouldn't be present on the network segment when the Amiga was on.  (Such as plugging the Amiga directly into the cable modem.)  Anyhow, your router handles DHCP, but it probably won't care if you pick another IP and assign it statically to the Amiga.  

The router probably hands out NAT addresses.  Something like 192.168.0.2, right?  Well, whatever IP address it gives your PC, just give the Amiga a number one higher.  So if the PC has 192.168.0.2, give the Amiga 192.168.0.3, and leave the rest of the settings identical to the PC.  It was probably the IP address conflict that stopped the Amiga from actually connecting properly.