trouble with networking 2 comps

Here is the situation:
Win XP pro SP3 on both computers. Computer A has wireless connection and ethernet connection. Computer B has ethernet only.
These computers are directly connected with a crossover ethernet cable.
At first, A would either have internet connectivity or file sharing with B, but not both. I was using a restore point to get internet access back after trying to connect with B at first.
I found advice to change the auto metrics to manual, with a value of 10 for the wireless connection (giving it priority?), then bridged the two connections on computer A, and now A can access both the internet and computer B consistently. Computer B cannot access computer A's files or the internet.

Pinging from computer pingB gives me:
C:\Documents and Settings\Administrator>ping 192.168.15.101
Pinging 192.168.15.101 with 32 bytes of data:

Request timed out.
Request timed out.
Request timed out.
Request timed out.

Ping statistics for 192.168.15.101:
Packets: Sent = 4, Received = 0, Lost = 4 (100% loss),

C:\Documents and Settings\Administrator>ping http://www.google.comPing request could not find host http://www.google.com. Please check the name and try again.

Pinging from A gives me:
C:\Documents and Settings\Scott>ping http://www.google.com
Pinging http://www.google.com [74.125.137.106] with 32 bytes of data:

Reply from 74.125.137.106: bytes=32 time=33ms TTL=48
Reply from 74.125.137.106: bytes=32 time=37ms TTL=48
Request timed out.
Reply from 74.125.137.106: bytes=32 time=53ms TTL=48

Ping statistics for 74.125.137.106:
Packets: Sent = 4, Received = 3, Lost = 1 (25% loss),
Approximate round trip times in milli-seconds:
Minimum = 33ms, Maximum = 53ms, Average = 41ms

C:\Documents and Settings\Scott>ping 192.168.15.112
Pinging 192.168.15.112 with 32 bytes of data:

Reply from 192.168.15.112: bytes=32 time<1ms TTL=128
Reply from 192.168.15.112: bytes=32 time=1ms TTL=128
Reply from 192.168.15.112: bytes=32 time<1ms TTL=128
Reply from 192.168.15.112: bytes=32 time<1ms TTL=128

Ping statistics for 192.168.15.112:
Packets: Sent = 4, Received = 4, Lost = 0 (0% loss),
Approximate round trip times in milli-seconds:
Minimum = 0ms, Maximum = 1ms, Average = 0ms

Any suggestions?