For the net001 failures, here are the execution times in seconds
for my JDK7-B109 testing:

$ get_tonga_test_times -f 900 vm-hprof-prod-*/tonga.output/Tonga.log.log
log: vm-hprof-prod-client-fast-comp.windows-i586/tonga.output/Tonga.log.log
    1011 nsk/hprof/options/net/net001 FAIL


log: vm-hprof-prod-client-fast-mixed.windows-i586/tonga.output/Tonga.log.log
log: vm-hprof-prod-client-prod-comp.windows-i586/tonga.output/Tonga.log.log
    1692 nsk/hprof/options/net/net001 FAIL


log: vm-hprof-prod-client-prod-mixed.windows-i586/tonga.output/Tonga.log.log
    1085 nsk/hprof/options/net/net001 FAIL


log: vm-hprof-prod-server-fast-comp.windows-i586/tonga.output/Tonga.log.log
    8579 nsk/hprof/options/net/net001 FAIL


log: vm-hprof-prod-server-fast-mixed.windows-i586/tonga.output/Tonga.log.log
    3774 nsk/hprof/options/net/net001 FAIL


log: vm-hprof-prod-server-prod-comp.windows-i586/tonga.output/Tonga.log.log
    25815 nsk/hprof/options/net/net001 FAIL


log: vm-hprof-prod-server-prod-mixed.windows-i586/tonga.output/Tonga.log.log
    1683 nsk/hprof/options/net/net001 FAIL

This testing was executed over a weekend and I wasn't around much to
dismiss the pop-ups. The Tonga timeout is set to 900 seconds, but
the vm-hprof-prod-server-prod-comp.windows-i586 failure ran for 7.17
hours!
During my baseline testing on JDK7-B108 and JDK7-B109, the following
tests failed in my WinXP configurations:

    nsk/hprof/options/net/net001
    nsk/hprof/options/net/net003

The tests generated a pop-up that stopped execution of the test suite
until the popup was dismissed.

My machine is a MacBook Pro:

  Model Name: MacBook Pro
  Model Identifier: MacBookPro5,2
  Processor Name: Intel Core 2 Duo
  Processor Speed: 2.8 GHz
  Number Of Processors: 1
  Total Number Of Cores: 2
  L2 Cache: 6 MB
  Memory: 4 GB
  Bus Speed: 1.07 GHz
  Boot ROM Version: MBP52.008E.B05
  SMC Version (system): 1.42f4
  Serial Number (system): W80040AF8YB
  Hardware UUID: AABAF561-9DCC-5311-868C-518EB18115E1
  Sudden Motion Sensor:
  State: Enabled

I'm running VMware Fusion 3.X and I have WinXP VMware client:

    Windows XP Professional, SP3
    two virtual processors enabled
    2GB of RAM enabled

I'm running the following version of Cygwin:

$ uname -a
CYGWIN_NT-5.1 oliver-lt 1.5.25(0.156/4/2) 2008-06-12 19:34 i686 Cygwin

I updated my Cygwin packages on 2010.03.31.

Update: I forgot to say that these popups do not occur with JDK7-B107 bits.
I've attached a screen snapshot of the popup as "java_popup.png".
The following SDK/JDK tests from the MISC_REGRESSSION subsuite
also failed with a pop-up in my WinXP configurations:

    sun/tools/jmap/Basic.sh

JTREG/JavaTest hung until the pop-up was dismissed.
The following SDK/JDK tests from the MM_REGRESSSION subsuite
also failed with two pop-ups in my WinXP configurations:

    com/sun/management/HotSpotDiagnosticMXBean/DumpHeap.sh

JTREG/JavaTest hung until the pop-ups were dismissed.
The following VM/NSK tests from the heapdump subsuite
pass with a pop-up in my WinXP configurations:

    heapdump/OnOOMToFile
    heapdump/OnOOMToFilePerm
    heapdump/OnOOMToPath

Tonga test harness hangs until the pop-ups are dismissed.
Note that these tests PASS, but cause the test harness to
hang or grind to a halt...